Final answer:
The king must be cautious about how he handles Hamlet due to Hamlet's popularity and the political implications of overtly aggressive action against him. Additionally, Hamlet's visible internal conflict and philosophical struggles reflect critical themes in Shakespeare's play.
Step-by-step explanation:
The question refers to the complexities of Hamlet's actions and the limitations placed upon him in navigating the monarchy and his own moral dilemma in Shakespeare's play. The king in Hamlet must not put the 'strong arm' onto Hamlet primarily because of the political and social ramifications. Hamlet is not only the son of the former king but also highly regarded by the people. This makes him somewhat protected against overt actions by the current king, Claudius. Additionally, Hamlet is experiencing a deep internal conflict that is exacerbated by the duplicity and immorality he perceives in the royal court, particularly in his mother and uncle. His struggles with action and inaction highlight a critical theme of the play, reflecting the disconnect between his intense emotions and the external world.
The literary critic Harold Bloom suggests that Hamlet is genuinely seeing his father's spirit, strengthening Hamlet's internal justification for his hesitancy to take decisive action. Meanwhile, Hamlet himself professes that strong emotions, such as viewing a ghost, are common human experiences, thereby challenging the remarks of his tutor, Polonius, who dismisses the supernatural encounter as imaginary. These complexities in Hamlet's character, a mix of rationalization and emotional turmoil, illustrate why the king must approach the situation with caution.