This is a terrific and very advanced use of chain-of-thought prompting. Many folks get frustrated when the first LLM response they get isn't the be-all, end-all answer. I have started to think of prompting like teaching a class of children (or CS students).

We shouldn't expect the right answer the first time. We should lead the LLM down the path to correctness. And we don't need to go all the way there -- just enough to get back to our real work.

While this seems counterintuitive, it's actually very useful in practice!