Those aren't good analogies. An LLM isn't like a xerox machine or a tape recorder. Again, the answers to the bar exam it passed weren't in its training data. Nor was the code it wrote for me.

I'm using the common, colloquial definition of reasoning. I don't think we need an academic treatise to say that passing the bar exam (without copying the answers) or writing code for a novel task requires reasoning.

You're right that we don't fully understand how the LLM is doing this, but that doesn't mean it isn't happening.