I would argue that's a false dichotomy. In your terms, there can be no purpose of me without purpose of action. And purpose of action requires selection from multiple viable options.
Those two usages are not mutually exclusive, I just don't know which one you are using (or if it is some other usage).
I'm not sure that there is any intrinsic purpose to anything, only ever purpose imbued.
I understand the word gets used that way, to describe some intrinsic meaning to a life, but the word being used that way doesn't mean the thing it describes exists.
To try and be a bit clearer let me write out the three usages I am aware of and you can say which you are talking about.
1. I picked up the apple with the purpose of eating it.
2. My purpose in life is to enjoy it and leave the world a better place than when I found it.
3. The purpose of humans is to colonise the universe.
1 is purpose of an action (the action is done for a reason), 2 is purpose I give myself (I choose what gives me meaning), 3 is intrinsic purpose (regardless of what anyone wants or thinks).
It’s also not clear if you are discussing “why I do something” (purpose of an action) or “why am I?” (purpose of me).