dad invited me to eat with him? what is the verb in this sentence

What is the "action"? What is somebody doing?

There are two verbs.

The predicate action verb, performed by the subject (Dad), is "invited". The infinitive "to eat" is part of an adverbial modifying phrase

The verb in the sentence "Dad invited me to eat with him" is "invited." To identify the verb in a sentence, you can ask yourself the question "What action is being performed?" In this case, the action being performed is the act of inviting, which is expressed by the verb "invited."