ChatGPT doesn't "grok" anything. It's simply picking the best next word one after the other. Unless your problem statement has statistical significance in its training data, bad results are expected.
Do you have a reason to believe that an LLM like GPT would be unable to learn how to reason?
I don't see how, given current implementation, an LLM can come up with an original thought or invent something novel. Statistics != reasoning.