Participants will receive either MK-1029 1 mg or 3 mg tablets (dose to be determined based on results of interim analysis from Part I) QD.

Participants will receive Montelukast 10 mg tablets QD and MK-1029 tablets (dose to be determined based on results of interim analysis from Part I) QD

Parts I-II: Participants will receive Montelukast 10 mg tablets QD

Parts I-II: Participants will receive Placebo tablets QD

The Daytime Symptom Score assessed daytime asthma symptoms. In the evening just before going to bed, participants scored their asthma symptoms for the period since arising by answering the following 4 questions in eDiaries: 1) How often did you experience asthma symptoms today?, 2) How much did your asthma symptoms bother you?, 3) How much activity could you do today? and 4) How often did your asthma affect your activities today? The 4 questions were scored on a 7-point scale (0=best to 6=worst) and averaged for a single score. The average change from baseline in DSS over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average DSS score during the placebo run-in period and the post-baseline value was the average DSS Score over Week 6 to Week 12.

Twice daily (upon arising and before going to sleep), participants recorded the total number of puff (actuations) of SABA used for asthma symptoms in their eDiaries. The number of SABA puffs used in one day was calculated based on eDiary entries as the sum of daytime and nighttime number of puffs of SABA. The average change from baseline over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) in the daily number of SABA puffs was estimated using a cLDA model. In the cLDA analysis, Baseline was the average number of SABA puffs used in one day during the placebo run-in period and the post-baseline value was calculated as the average number of SABA puffs used in one day over Week 6 to Week 12.

The number of nights per week (between consecutive visits) that a participant awakened with asthma was based on eDiary entries and was calculated by dividing the number of nights a participant awakened with asthma (positive responses of once, more than once, awake "all night") by the total number of nights (all responses) and then multiplying by 7 (standardized to a 7-day period). The average change from baseline in number of nocturnal awakenings over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average number of nocturnal awakenings during the placebo run-in period and the post-baseline value was calculated as the average number of nocturnal awakenings over Week 6 to Week 12.

PEF was defined as a person's maximum speed (rate) of expiration as measured with a peak flow meter in liters per minute. Participants performed triplicate PEF measurements twice daily using a PEF meter, in the AM upon rising and in the PM immediately before study drug administration at bedtime. All three values were recorded and the average of the best morning PEF and the best evening PEF for each day (AM/PM) was determined through the e-Diary. The average change from Baseline in AM/PM PEF over the last 6 weeks of a 12-week treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average AM/PM PEF value during the placebo run-in period and the post-baseline value was calculated as the average AM/PM PEF over Week 6 to Week 12.

The AQLQ(S) is a 32-item questionnaire with questions on 4 domains (asthma symptoms, activity limitation, emotional function and environmental stimuli) over the previous 2 weeks. Responses were scored on a 7-point scale (1=worst to 7=best). Each domain score is defined as the average score of all answered questions in that domain. The AQLQ(S) Overall Score is defined as the average of all available item scores (1=worst to 7=best). The changes from baseline are presented for the overall scores and the individual domain scores. Baseline was the last measurement taken prior to the first double-blind study drug. The ending values were calculated as the average AQLQ(S) Overall Score and domain scores at Week 12 of a 12-week treatment period. Statistical analyses are provided for the AQLQ(S) Overall Scores only.

The AQLQ(S) is a 32-item questionnaire with questions on 4 domains (asthma symptoms, activity limitation, emotional function and environmental stimuli) over the previous 2 weeks. Responses were scored on a 7-point scale (1=worst to 7=best). Each domain score is defined as the average score of all answered questions in that domain. The AQLQ(S) Overall Score is defined as the average of all available item scores (1=worst to 7=best). The percentage of participants who experienced a ≥0.5 increase in AQLQ(S) Overall and Domain Scores at Week 12 compared to baseline was calculated using the Miettinen and Nurminen (MN) method. Statistical analyses are provide for the AQLQ(S) Overall Score response rate only.

The ACQ is a validated 6-item measure of asthma control to evaluate asthma control in response to therapy. Participants evaluate their asthma over the previous week by answering 6 questions: How often were you woken by your asthma during the night? How bad were your asthma symptoms when you woke up in the morning? How limited were you in your activities because of your asthma? How much shortness of breath did you experience because of your asthma? How much of the time did you wheeze? How many puffs/inhalations of short-acting bronchodilator have you used each day? Each response to a question was scored on a 7-point scale (0=best to 6=worst). The ACQ score is the average of the scores for the 6 items. Change from baseline to Week 12 in ACQ was estimated using a cLDA model. In the cLDA analysis, the Baseline value was the last measurement taken prior to the first double-blind study drug and the post-baseline value was calculated as the average ACQ Score at Week 12.

The ACQ is a validated 6-item measure of asthma control to evaluate asthma control in response to therapy. Participants evaluate their asthma over the previous week by answering 6 questions: How often were you woken by your asthma during the night? How bad were your asthma symptoms when you woke up in the morning? How limited were you in your activities because of your asthma? How much shortness of breath did you experience because of your asthma? How much of the time did you wheeze? How many puffs/inhalations of short-acting bronchodilator have you used each day? Each response to a question was scored on a 7-point scale (0=best to 6=worst). The ACQ score is the average of the scores for the 6 items. The percentage of participants who experienced a ≥0.5 decrease in ACQ Score at Week 12 compared to Baseline was calculated using the MN method.

An asthma attack was defined as asthma symptoms during the previous 24 hours requiring one or more of the following: corticosteroid use (systemic), unscheduled visit to the doctor or urgent care clinic, unscheduled visit to the emergency department or hospitalization. Information on asthma attacks was recorded throughout the study in the participant's e-Diary, and an Analysis of Variance (ANOVA) was used to calculate the average percentage of asthma attack days over Week 6 to Week 12 of a 12-week treatment period.

Participants receive MK-1029 two 30 mg tablets QD for 12 weeks

Participants receive MK-1029 150 mg tablets QD for 12 weeks

Participants receive Montelukast 10 mg tablets QD for 12 weeks

Participants receive Placebo tablets QD for 12 weeks

Total of all reporting groups

The Asthma Phenotype in this study was defined as either "Th2-High" or "Th2-Low," based on measurements of asthmatic inflammation. Th2-High was defined according to the following 2 criteria at Visit 1: a peripheral-blood absolute eosinophil count ≥ 0.30 X 10^9/liters(L), and/or a peripheral-blood absolute eosinophil count ≥0.14 X 10^9/L with serum total IgE ≥100 IU/mL. Th2-Low was operationally defined as meeting neither of these criteria.

All participants who received ≥1 dose of study drug.

Participants receive MK-1029 30 mg tablets QD for 12 weeks

Participants will receive MK-1029 two 30 mg tablets QD for 12 weeks

Participants will receive MK-1029 150 mg tablets QD for 12 weeks

Participants will receive Montelukast 10 mg tablets QD for 12 weeks

Participants will receive Placebo tablets QD for 12 weeks

An AE is defined as any unfavorable and unintended change in the structure, function, or chemistry of the body temporally associated with the use of the study drug, whether or not considered related to the use of the study drug. Any worsening (i.e., any clinically significant adverse change in frequency and/or intensity) of a pre-existing condition which is temporally associated with the use of the study drug, is also an AE.

All randomized participants who received ≥1 dose of study drug.

An AE is defined as any unfavorable and unintended change in the structure, function, or chemistry of the body temporally associated with the use of the study drug, whether or not considered related to the use of the study drug. Any worsening (i.e., any clinically significant adverse change in frequency and/or intensity) of a pre-existing condition which is temporally associated with the use of the study drug, is also an AE.

All randomized participants who received ≥1 dose of study drug.

An asthma exacerbation day was defined as a day with ANY of the following: a decrease from Baseline in morning (AM) Peak Expiratory Flow (PEF) of more than 20%, an AM PEF of less than 180 liters (L)/min, an increase in Short Acting Beta2 Agonist (SABA) use of more than 70% (and a minimum increase of at least 2 puffs), an increase from Baseline in Daytime Asthma Symptom Score of more than 50%, an overnight asthma symptom of: Awake "all night", or an asthma attack. Information on asthma exacerbation days was recorded throughout the study in the participant's electronic diary (e-Diary), and an Analysis of Variance (ANOVA) was used to calculate the average percentage of days with asthma exacerbations over Week 6 to Week 12.

TH2-High participants who received ≥1 study drug dose and had asthma exacerbation data.

The Daytime Symptom Score assessed daytime asthma symptoms. In the evening just before going to bed, participants scored their asthma symptoms for the period since arising by answering the following 4 questions in eDiaries: 1) How often did you experience asthma symptoms today?, 2) How much did your asthma symptoms bother you?, 3) How much activity could you do today? and 4) How often did your asthma affect your activities today? The 4 questions were scored on a 7-point scale (0=best to 6=worst) and averaged for a single score. The average change from baseline in DSS over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average DSS score during the placebo run-in period and the post-baseline value was the average DSS Score over Week 6 to Week 12.

TH2-High participants who received ≥1 study drug dose and had DSS data.

Twice daily (upon arising and before going to sleep), participants recorded the total number of puff (actuations) of SABA used for asthma symptoms in their eDiaries. The number of SABA puffs used in one day was calculated based on eDiary entries as the sum of daytime and nighttime number of puffs of SABA. The average change from baseline over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) in the daily number of SABA puffs was estimated using a cLDA model. In the cLDA analysis, Baseline was the average number of SABA puffs used in one day during the placebo run-in period and the post-baseline value was calculated as the average number of SABA puffs used in one day over Week 6 to Week 12.

TH2-High participants who received ≥1 study drug dose and had SABA usage data.

The number of nights per week (between consecutive visits) that a participant awakened with asthma was based on eDiary entries and was calculated by dividing the number of nights a participant awakened with asthma (positive responses of once, more than once, awake "all night") by the total number of nights (all responses) and then multiplying by 7 (standardized to a 7-day period). The average change from baseline in number of nocturnal awakenings over the last 6 weeks of the 12-week-treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average number of nocturnal awakenings during the placebo run-in period and the post-baseline value was calculated as the average number of nocturnal awakenings over Week 6 to Week 12.

TH2-High participants who received ≥1 study drug dose and had nocturnal awakening data.

PEF was defined as a person's maximum speed (rate) of expiration as measured with a peak flow meter in liters per minute. Participants performed triplicate PEF measurements twice daily using a PEF meter, in the AM upon rising and in the PM immediately before study drug administration at bedtime. All three values were recorded and the average of the best morning PEF and the best evening PEF for each day (AM/PM) was determined through the e-Diary. The average change from Baseline in AM/PM PEF over the last 6 weeks of a 12-week treatment period (visits at Week 6, Week 8, Week 10 and Week 12) was estimated using a cLDA model. In the cLDA analysis, baseline was the average AM/PM PEF value during the placebo run-in period and the post-baseline value was calculated as the average AM/PM PEF over Week 6 to Week 12.

TH2-High participants who received ≥1 study drug dose and had AM/PM PEF data.

The AQLQ(S) is a 32-item questionnaire with questions on 4 domains (asthma symptoms, activity limitation, emotional function and environmental stimuli) over the previous 2 weeks. Responses were scored on a 7-point scale (1=worst to 7=best). Each domain score is defined as the average score of all answered questions in that domain. The AQLQ(S) Overall Score is defined as the average of all available item scores (1=worst to 7=best). The changes from baseline are presented for the overall scores and the individual domain scores. Baseline was the last measurement taken prior to the first double-blind study drug. The ending values were calculated as the average AQLQ(S) Overall Score and domain scores at Week 12 of a 12-week treatment period. Statistical analyses are provided for the AQLQ(S) Overall Scores only.

TH2-High participants who received ≥1 study drug dose and had AQLQ(S) data.

The AQLQ(S) is a 32-item questionnaire with questions on 4 domains (asthma symptoms, activity limitation, emotional function and environmental stimuli) over the previous 2 weeks. Responses were scored on a 7-point scale (1=worst to 7=best). Each domain score is defined as the average score of all answered questions in that domain. The AQLQ(S) Overall Score is defined as the average of all available item scores (1=worst to 7=best). The percentage of participants who experienced a ≥0.5 increase in AQLQ(S) Overall and Domain Scores at Week 12 compared to baseline was calculated using the Miettinen and Nurminen (MN) method. Statistical analyses are provide for the AQLQ(S) Overall Score response rate only.

TH2-High participants who received ≥1 study drug dose and had AQLQ(S) data at Week 12.

The ACQ is a validated 6-item measure of asthma control to evaluate asthma control in response to therapy. Participants evaluate their asthma over the previous week by answering 6 questions: How often were you woken by your asthma during the night? How bad were your asthma symptoms when you woke up in the morning? How limited were you in your activities because of your asthma? How much shortness of breath did you experience because of your asthma? How much of the time did you wheeze? How many puffs/inhalations of short-acting bronchodilator have you used each day? Each response to a question was scored on a 7-point scale (0=best to 6=worst). The ACQ score is the average of the scores for the 6 items. Change from baseline to Week 12 in ACQ was estimated using a cLDA model. In the cLDA analysis, the Baseline value was the last measurement taken prior to the first double-blind study drug and the post-baseline value was calculated as the average ACQ Score at Week 12.

TH2-High participants who received ≥1 study drug dose and had ACQ data.

The ACQ is a validated 6-item measure of asthma control to evaluate asthma control in response to therapy. Participants evaluate their asthma over the previous week by answering 6 questions: How often were you woken by your asthma during the night? How bad were your asthma symptoms when you woke up in the morning? How limited were you in your activities because of your asthma? How much shortness of breath did you experience because of your asthma? How much of the time did you wheeze? How many puffs/inhalations of short-acting bronchodilator have you used each day? Each response to a question was scored on a 7-point scale (0=best to 6=worst). The ACQ score is the average of the scores for the 6 items. The percentage of participants who experienced a ≥0.5 decrease in ACQ Score at Week 12 compared to Baseline was calculated using the MN method.

TH2-High participants who received ≥1 study drug dose and had ACQ data at Week 12.

An asthma attack was defined as asthma symptoms during the previous 24 hours requiring one or more of the following: corticosteroid use (systemic), unscheduled visit to the doctor or urgent care clinic, unscheduled visit to the emergency department or hospitalization. Information on asthma attacks was recorded throughout the study in the participant's e-Diary, and an Analysis of Variance (ANOVA) was used to calculate the average percentage of asthma attack days over Week 6 to Week 12 of a 12-week treatment period.

TH2-High participants who received ≥1 study drug dose and had asthma attack data.

Participants receive MK-1029 30 mg tablets QD for 12 weeks

Participants receive MK-1029 two 30 mg tablets QD for 12 weeks

Participants receive MK-1029 150 mg tablets QD for 12 weeks

Participants receive Montelukast 10 mg tablets QD for 12 weeks

Participants receive Placebo tablets QD for 12 weeks

Difference in LS means for percent of asthma exacerbation day over Week 6 through Week 12: MK- 1029 60 mg vs. Placebo. ANOVA model includes the terms for treatment groups and prior ICS use (Yes/No). Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for percent of asthma exacerbation day over Week 6 through Week 12: MK- 1029 150 mg vs. Placebo. ANOVA model includes the terms for treatment groups and prior ICS use (Yes/No). Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for percent of asthma exacerbation day over Week 6 through Week 12: Montelukast vs. Placebo. ANOVA model includes the terms for treatment groups and prior ICS use (Yes/No). Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline to Week 12 in DSS: MK-1029 60 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK- 1029 or Montelukast).

Difference in LS means for average change from Baseline to Week 12 in DSS: MK-1029 150 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline to Week 12 in DSS: Montelukast vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in SABA use: MK-1029 60 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in SABA use: MK-1029 150 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in SABA use: Montelukast vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in nocturnal awakenings: MK-1029 60 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in nocturnal awakenings: MK-1029 150 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in nocturnal awakenings: Montelukast vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in AM/PM PEF: MK-1029 60 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).

Difference in LS means for average change from Baseline over Week 6 to Week 12 in AM/PM PEF: MK-1029 150 mg vs. Placebo. cLDA model includes terms for visit as categorical variable, prior ICS use (Yes/No) and treatment by visit. Negative differences are in favor of the first treatment group in the comparison (MK-1029 or Montelukast).