From the link I posted before, under section 4.2:
He may use his single Action before, after, or in the middle of his Movement, but he only gets one, so he must spend it wisely.
However, the way that I read the rules, entering Close Combat ends the creation's regular turn (Movement and Action phase) and they are only in Close Combat. The rules say:
...they are both entered into Close Combat (5.2: Close Combat) and the minifig’s Movement is over for the turn.
So if you attack Close Combat, the answer is no. If you make an action that does not put you in Close Combat, then the answer to your question is yes.