While Harmonie was busy tracking Chleo's whereabouts, Max repeatedly teleported to places to look for Chleo since hearing his girl disappear. He teleported so much that it drained almost all of his energy.
At first, Max thought maybe Chleo was busy somewhere and carelessly dropped the bracelet and left her phone. That's why he only had Falcon search above while tracking the energy of the seed he planted in Chleo's fingers.
But when Falcon told him that he didn't feel Chleo's presence in the hotel at all, Max got even more worried. He teleported back and forth to the places the girl frequented while living in this city in vain. He couldn't find Chleo wherever he looked.
Max didn't look for her out of town because he believed Chleo wouldn't leave this city. Chleo was one of the people in charge of tonight's gala show, so it was impossible for the girl to abandon her responsibilities as an event committee member.