Study to Evaluate the Effectiveness and Safety of MK-1029 in the Treatment of Persistent Asthma That is Not Controlled With Montelukast (ML) in Adults (MK-1029-011)

The purpose of this study is to evaluate the effect of MK-1029 on lung function in the treatment of adults who have persistent asthma that is uncontrolled with the use of montelukast (ML). Participants will use randomized study drug (either MK-1029 or placebo) for two separate 4-week treatment periods. All participants will also use ML during the treatment periods. The primary hypothesis is that MK-1029 is superior to placebo in change from baseline in forced expiratory volume in one second (FEV1) at the end of the 4-week treatment period.