“Compound verb” merely refers to a subject doing more than one thing. Compound verbs are connected by conjunctions and commas.
I baked bread and made soup.
The subject I does two things: bake and make; these are compound verbs.
We ate potatoes chips and drank soda.
The kids painted pictures, played games, and had a water fight.
Mary should have danced or sung a song, but not both.