Sorry but no, you're quite wrong.
You're broadly describing very early LLMs, not modern commercially-available ones.
Modern ones cannot "plan" in every sense of the word - they cannot have intent to do something and they cannot set goals.
They can, though, engage in the act of planning, based on a prompt, and to a specified end goal.
E.g., in terms of something like planning a classroom activity, if you gave a prompt to an early LLM then yes, it would merely generate a plan (or at least, something that resembles one). It would analyze language patterns and predict an appropriate response on that basis alone.
If you gave the same input to a modern LLM, though, it would engage in the functional act of "planning", using a multi-step process.
Instead of simpy analyzing language patterns of the prompt, it would analyze the actual content of it, differentiating between context, specifications and goals to determine the actual task it is required to perform, and to what parameters.
It will then determine the steps required to solve the "problem" (how to develop the lesson plan).
For example, it may determine that it has insufficient information about the topic of the planned activity, and (without further prompt) engage in research by retrieval from available data sources. E.g., it identifies information "gaps" in the initial prompt it was given, then takes steps to fill them.
It then, through application of logic to the data (the initial input and additional data known or retrieved), constructs a plan that is tailored to the initial prompt in a meaningful way.
If you don't believe me, ask something like Microsoft Copilot (which doesnt need to be downloaded) to plan a week-long holiday for you, where you want to visit multiple points of interest across a country or region (you can specify places, and/or ask for recommendations, and/or tell it your likes and limitations).
Once it gives you a suggested itinerary, ask it to provide any particular sources it drew upon or, if it didnt scrape from similar sources, what data and methodologies it employed.
LLMs don't "think" and do not "understand" in a human sense, but they do analyze and problem solve and, in a real but non-human sense, "reason". You are also wrong to say that they don't "invent" - they do (but based on executing a command, not with intent).