In the play, is Hamlet a man of action or a man of thought? Does that change throughout the play? Why or how?
Through almost the entire play, Hamlet is tied up in his own head. He struggles with the decision to continue living, given the suspected murder of his father and the flight to "incestuous sheets" when his mother marries Claudius so soon after Hamlet Sr. is killed. He suspects that Claudius is behind his father's death, but he can't prove it and so he can't decide whether to kill Claudius or not.
When it becomes clearer that Claudius did in fact kill his father and Hamlet has the opportunity to kill him while Claudius is praying, he cannot do it as he again debates the effectiveness of killing a murderer while he is communing with God. He struggles as well with what to do about Ophelia. He has feelings for her but cannot pursue them given that he is so tied up in knots about his father's murder and everything else.
His change to a man of action comes only at the very tail end of the play as the certainty of what Claudius did becomes clear and Claudius murders his mother. At this point he takes revenge upon Claudius but is killed in the process, perhaps suggesting that his change to a man of action came far too late.