It's not about (in-)determinism really, it's about the algorithm part.

An algorithm that does something can in principle be ran by someone who doesn't know what the algorithm does. You could have a kid calculate an integral by giving it a sequence of directions whose purpose it doesn't understand (e.g. cut out some cardboard that matches the shape, put it on one side of the scale, place enough unit cardboard pieces on the other side until they are even, then tell me how many pieces you put).

Reasoning has more to do with how the problem came about. A person had to come against a certain problem, figure out a way in which they can solve it, then apply the (perhaps algorithmic) solution. The algorithmic part is only an artifact.

There is a difference between determinism in the sense of given a certain input, you allways get a certain output, and determinism in the sense of given a certain input, and knowledge of the sub universe in which the problem applies, get a certain output.

I.e an agent that can reason can deterministically figure out that the most probable way of getting information to complete the answer would be to go out on google and do searches, but we don't deterministically know what the information that exists at that point and time on google, so the answer could be different.

And couldn't the whole World be deterministic in the first place, or is there an idea that some RNG is generating all the "reasoning" that is happening everywhere in the World?

And if it's RNG, how could RNG be possibly creating all this reasoning (like some people want to believe quantum mechanics possibly enables consciousness on some odd levels).