This is basically the LLM modulo approach recommended by Prof. Subbarao Kambhampati. Interesting but only works mostly for problems that have some math/first degree logic puzzle at their heart. Will fail at improving perf at ARC-AGI for example...
Difficult to mimic reasoning by basic trial and error then hoping for the best:
https://www.lycee.ai/blog/why-sam-altman-is-wrong