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If I were to do this, I would ask the LLM to come up with a model that would predict the output and then to estimate the parameters and calculate the prediction (and show the work).

For all we know, this is what's happening inside the black box (if it's really simulating a super forecaster), but from experience, it's easier to get what I want from LLMs if I have it talk a little about what it's doing.

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A better task would be to ask the LLM what information they need to check to have a better guess and offer constraints like publicly available information or information that doesn’t cost more than a certain amount to get.

A real expert isn’t someone who knows the calorific coefficient of water off the top of their head but knows it’s relevant information to look up when asked if a cargo ship full of feedstock could burn and vaporize the water in the Suez Canal.

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