No. The entirety of an LLMs output is predicated on the frequencies of patterns in its training data, moulded by the preferences of its trainers through RLHF. They're not capable of reasoning, but they can hallucinate language that sounds and flows like reasoning. If those outputs are fed into an interpreter, that can result in automated behavior. They're not capable of out of distribution behavior or generation (yet), despite what the AI companies would like you to believe. They can only borrow and use concepts from that which they've been trained on, which is why despite LLMs seemingly getting progressively more advanced, we haven't really seen them invent anything novel of note.
This is a non-answer that doesn't explain any difference in capabilities between GPT-3.5 and Claude 4 Opus.
Yes, I too am familiar with the 101 level of understanding, but I've also heard of LLMs doing things that stretch that model. Perhaps that's just a matter of combining things in their training data in unexpected ways, hence the second half of my question.