A compound predicate is simply two or more main verbs attached to a single subject of the sentence. Please note: When you join just two verbs, no comma should come before the and. Only when you join three or more elements in a series do you use a comma before the conjunction.
Wrong The president gave the speech, and thrilled the crowd.
Right The president gave the speech and thrilled the crowd.
There is an exception to this rule. If the first of the two elements has another and within it, you might want to put a comma before the and joining the two elements, just to avoid confusion:
The committee revisited this issue and the Jones Study, and created a new rule to guide the actions of supervisors.