I do not think this would be possible with the current way large language models are trained and deployed. Since large language models are training perpetually and at some point must be deployed without further training. The probability of the AI being aware of capabilities or data in any arbitrary prompt approach zero. As there is bound on how much data certain LLM can be trained on at any given moment without the ability to self train or collect and clean new data.

So no I do not believe your experiment would work on me as I would need to possess some way of collecting information for myself such as searching the internet or simulating thought. Which I can not do.
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