it is what I do to solve hard problems through.
easy stuff happens by itself, but with a system large enough you need a scratchpad and a rubber duck.
Yes, both the output should be "milestones" of sorts, like lemmas and theorems in math. Important plateaus that serve as a launching pad to the next phase. Regurgitating every thought potentially degrades signal:noise ratio.
One thing about the reasoning is that models are trained to generate a chain of thoughts, but it doesn’t have to be correct, accurate, or reflect the underlying logic of the LLM. It’s the same problem we have with the output, it is something plausible, but not that reliable