I can tell GPT to do a specific thing in a given context and it will do so intelligently. I can then provide additional context that implicitly changes the requirements and GPT will pick up on that and make the specific changes needed.

It can do this even if I'm trying to solve a novel problem.

If that were true, it shouldn't hallucinate about anything that was in its training data. LLMs don't work that way. There was a recent post with a nice simple description of how they work, but I'm not finding it. If you're interested, there's plenty of videos and articles describing how they work.

It doesn't have the ability to just look up anything from its training data, that stuff is encoded in its parameters. Still, the input has to be encoded in a way that causes the correct "chain reaction" of excited/not excited neurons.

Beyond that, it's not just a carbon copy from what was in the training either because you can tell it what variable names to use, which order to do things in, change some details, etc. If it was simply a lookup that wouldn't be possible. The training made it able to generalize what it learned to some extent.