If I'm being completely honest, now that I've woken up with a fresh mind, I have no idea where I was going with that last part. Giving LLMs access to tools like running code so that they can fact check or whatever is a really good idea (that is already being tried) but I don't think it has anything to do with the problem at hand.

The real key issue (I think) is getting AI to keep learning and iterating over itself past the training stage. Which is actually what many people call AGI/the "singularity".