My understanding of the "purpose" of CoT, is to remove the wild variability yielded by prompt engineering, by "smoothing" out the prompt via the "thinking" outp

My understanding of the "purpose" of CoT, is to remove the wild variability yielded by prompt engineering, by "smoothing" out the prompt via the "thinking" output, and using that to give the final answer. Thus you're more likely to get a standardized answer even if your query was insufficiently/excessively polite.