> You can come up with complicated definitions of "core reasoning" where this doesn't count

Did we read the same response? It did write a lot of reasons, but didn't do any reasoning at all, it just suddenly wrote "5" here

    So, I’ll count the 5 occurrences of "i" in the word.

There was no reasoning at all to arrive at 5, so no your example just proves how these models are great at faking reasoning.