I happened to meet him y

I happened to meet him yesterday .

Is the verb happen or meet ? according to how to identify a predicate redicates are verbs that express the action performed by the subject or the subject's state of being .
isn't the action 'meet '? but ,if the predicate is meet, why changed 'happen' to 'happened' show the past tense ?
i'm confused ! please help . thank you !