What plan does hamlet reveal to the auidence once he is alone on stage?

In his famous "To be or not to be" soliloquy in Act 3, Scene 1, Hamlet reveals his plan to feign madness. He explains to the audience that he is putting on a show of insanity, but this is a calculated act designed to further his investigation into his father's murder and to manipulate those around him. He believes this façade will allow him to observe Claudius and others without suspicion, giving him the opportunity to gather evidence and ultimately avenge his father's death.

Here's a breakdown of Hamlet's reasoning:

* He doesn't want to reveal his true intentions: Hamlet is suspicious of those around him and doesn't trust anyone except Horatio. He fears that if he openly expresses his desire for revenge, he could be betrayed or silenced.

* He needs time to gather information: He wants to confirm Claudius' guilt and ensure he can convincingly expose him.

* He wants to manipulate Claudius: By acting mad, Hamlet hopes to provoke Claudius into revealing his guilt, potentially giving him the opportunity to act decisively.

This plan, while seemingly erratic, is carefully crafted by Hamlet and plays a significant role in driving the plot of the play forward.