As an aside, do bear in mind as soon as you go down the road of heavily criticising the LLM like this for a mistake, all bets are off until you start a fresh conversation. Filling the context with “you are useless” will almost certainly cause it to lean into its mistakes, not learn from them.
Ultimately, getting LLMs to “admit” to failings doesn’t really mean all that much, because they’ll say whatever seems plausible in the context.
ChatGPT confesses
See: Why Patience is a Virtue (or: How to Be Nice to Your LLM)