Telling the LLM to walk through the response, step by step is a prompt engineering thing though.
It is. Studied in the literature under the name "chain of thought" (CoT), I believe. It's still subject to the limitations I mentioned. (Though the output is more persuasive to a human even when the answer is the same, so you should be careful.)
You could make the user interface display the output more slowly "when it is unsure", but that'd show you the wrong thing: a tie between "brilliant" and "excellent" is just as uncertain as a tie between "yes" and "no".