I think “chain-of-thought” LLMs, with access to other tools like Python, already demonstrate two types of “thinking”.
We can query an LLM a simple question like “how many ‘r’ are in the word strawberry”, and an LLM with know access to tools will quite confidently, and likely incorrectly, give you an answer. There’s no actual counting happening, and any kind of understanding of the problem, the LLM will just guess an answer based on its training data. But that answer tends to be wrong, because those types of queries don’t make up a large portion of its training set, and if they do, there’s a large body of similar queries with vastly different answers, which ultimately results in confidentiality incorrect outputs.
But provide an LLM tools like Python, and a “chain-of-thought” prompt that allows it to recursively re-prompt itself, while also executing external code and viewing the outputs, and an LLM can easily get the correct answer to query “how many ‘r’ are in the word strawberry”. By simply writing and executing some Python to compute the answer.
Those two approaches to problem solving are strikingly similar to intuitive vs analytical thinking in humans. One approach is driven entirely by pattern matching, and breaks down when dealing with problems that require close attention to specific details, the other is much more accurate, but also slower because directed computation is required.
As for your hypothetical “weather AI”, I think it’s pretty easy to imagine an AGI capable of confidently predicting the weather tomorrow, not be capable of understanding how it computed the prediction, beyond a high level hand wavy explanation. Again, that’s basically what LLM do today, confidently make predictions of the future, with zero understanding of how or why they made those predictions. But you can happily ask an LLM how and why it made a prediction, and it’ll give you a very convincing answer, that will also be a complete and total deception.