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.