> Do we see signs of reasoning or is it anthropomorphism?
This is the part that so many folks just don't seem to understand (probably because it's been labeled as "thinking" or "reasoning" mode, and people assume that words have meaning). It's not reasoning or thought. It's spewing tokens pretending to "think", but it's actually just generating extra "context" to help the final answer be more coherent. The model isn't doing anything it doesn't already do. It's just doing more of it to improve the quality of the final answer displayed to the user.
Honestly, people need to get over this debate. It's pretty irrelevant in a lot of cases. When people ask "what is the model thinking?", they're really asking "what caused the model to produce this response (as opposed to a bunch of other plausible ones)?"
Whether it's thinking or word prediction or whatever you want to call it, people are trying to understand the causal chain.
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.