Well, compound verbs are supposed to be parallel. Meaning they have the same tense, person, and so on.
Here’s an example of not doing it:
So this (last panel) is a compound verb: “We should have bought and gave.” (shudder)
Gave??? Nah. Given! He started with a present perfect, so he should have finished with the present perfect, (should have) given, not the simple past, gave.
Don’t you do that.