[jmmcd]

> Reasoning properly is at least operating through processes that output correct results.

Human "reasoning" (ie speech or self-talk that sounds a bit like reasoning) often outputs correct results. Does "often" fit the definition?

> Which problems that demand producing correct solutions could be solved by a processor which could not solve a "detective game"?

For example, "what colour is the sky right now?". A lot of people could solve this (even if they haven't looked outside), and so could a lot of language models, which can't solve this detective game.

[mdp2021]

> Does "often" fit the definition?

No: "proper reasoning" is that process which given sufficient input will surely bring to a correct output owing to the effectiveness of its inner workings.

> what colour is the sky right now

That is not a general problem solver, and "output the most common recorded reply to a question" is certainly not a general problem solver, and the responses from the box indicated will easily be worthless for all special cases in which the question will make sense.