You're describing a process by which a 'thinking' entity uses cognition to refine a solution to a stated problem. That's a lot of words so usually we shorten this to 'reasoning'.

Do LLMs 'think'? I 'think' they do in a way. I don't really know how I think myself but I know I do and therefore I am (thanks, Descartes). I have a somewhat better grasp of the way LLMs 'think'. They do so sequentially, building a chain of descriptors which best fit the problem and the preceding descriptors. I suspect I do something not entirely dissimilar- i.e. I imagine 'worlds' which are like the current one changed in some way so they the problem I'm working on is reduced, then refine those until it is resolved - but in a massively parallel way.

Fine. Whatever. I give up. LLMs think. Believe what you want. I literally no longer care, and this argument is beyond exhausting. Go ask the LLM to explain itself to you. It will happily spew out a pretty solid explanation of the details and math involved if you ask it the right questions in the right way. It'll also happily play along with you if you want to roleplay that it is an actual thinking machine. It's designed that way. But hey, whatever. It's a thinking intelligent machine and we're all doomed. I accept that my many decades of working with and learning about computers was wasted and I know nothing about them at all.