A prompting hack: after each message from the LLM reply "Did you make a mistake in your last message?".

LLMs are better at analyzing their response after the fact than when it's unspooling its answer.

This is true even if it's the same LLM that generated the text.

When it's generating text, it's YOLOing it token-by-token, it can accidentally back itself into a corner that it can't correct.

But after the fact it can say "yeah, that got stuck in a corner, here's the way out of it" and do a better job the next time.