The thing to keep in mind in all these discussions about LLM planning and reasoning is that, when experts on planning and reasoning say that LLMs can't do planning and reasoning they have a very different, formal definition of those things in mind, than everybody else who hasn't studied them. Even some of the research papers on planning and reasoning with LLMs play very fast and loose with the use of those words and that's probably why there are so many positive results that later prove to be duds.
Now is probably a good time to re-educate computer scientists and AI researchers about planning and reasoning.
Wikipedia has a very short introduction to STRIPS planning:
https://en.wikipedia.org/wiki/Stanford_Research_Institute_Pr...
And here's a more comprhensive, but still short, introduction to automated planning and scheduling in general: