Not only that! LLM can also learn how to repeatedly apply f() for certain arguments, and run the shortcut. Sometimes, the shortcut learned is not actually repeated application of f(), which breaks semantic soundness of LLM's reasoning chain.

These shortcuts can greatly help reasoning, but they are not guaranteed to be sound. So yeah, in that case, LLMs are reasoning right (using shortcuts) for the wrong reasons (learning them from data instead by running actual repeated application and memoizing the resulting rule).