Earlier quoted context omitted.
The LLM does not "have" a plan. Arguably there's reason to believe it comes up with a plan when it is computing token propabilities, but it does not store it between tokens. I.e. it doesn't possess or "have" it. It simply comes up with a plan, emits a token, and entirely throws all its intermediate thoughts (including any plan) to start again from scratch on the next token.
I believe saying the LLM has a plan is a useful anthropomorphism for the fact that it does have hidden state that predicts future tokens, and this state conditions the tokens it produces earlier in the stream.
I know nothing about how things work at that level, so these might not even be reasonable questions.