It's interesting that humans would also benefit from the "chain of thought" type reasoning. In fact, I would argue all students studying math will greatly increase their competence if they are required to recall all relevant definition and information before using it. We don't do this in practice (including teachers and mathematicians!) because recall is effortful, and we don't like to spent more effort than necessar…
I wasn't amazing at maths research (did a PhD and post-doc and then gave up) but my experience was that it was partly thinking hard about things and grappling with what was going on and trying to break it down somehow, but also scanning everything you know related to the problem, trying to find other problems that resemble it in some way that you can steal ideas from etc.