Hamlet does not kill Claudius when he sees him in Act three, scene three because he believes that Claudius is praying and Hamlet believes that if he would've killed Claudius while he was praying that his soul would go to Heaven. Later in Act three, scene four Hamlet killed Polonius because at the time Hamlet was explaining the circumstances of his father's death to his mother and Polonius was eavesdropping on the conversation. Hamlet noticed him and believing that it was Claudius and now was his time to strike he stabbed Polonius through the curtains. I believe that there is an argument that Hamlet is both a man of thought and a man of action. Hamlet is a man of thought because as he noticed Claudius "praying" he thought about the situation
