Hey Sir, try this, change the name of the things, and try to generate a plan, you will understand why they can't plan. They can generate plan, but they are not capable of planning.
Plan retrieval and planning are not the same thing. It is well proven in blocks world, how poorly LLMs perform in planning.
Yes, LLMs can help in planning, in LLM-modulo setting where you have external verifiers. But on their own, they can't.
Highly recommended, please read Prof. Subbarao's work from Arizona State University.
And still no one ever answers to me, let's imagine a problem where the answer is of two words. But it's an exponential problem, so, do you think LLM will take exponential time to generate both the words or will it do in constant time?