If an LLM arrives at the same output a human does given input and the output is sufficiently low probability to happen by random chance or association then it fits the term reasoning insofar as the maximum extent in which we understand it.
Given that we don't know what's going on the best bar is simply my matching input and output and making sure it's not using memory or pattern matching or random chance. There are MANY prompts that meet this criteria.
Your thoughts and claims are to be honest just flat out wrong. It’s just made up because not only do you know what the model is doing internally you don’t even know what you or any other human is doing. Nobody knows. So I don’t know why you think your claims have any merit. They don’t and neither do you.