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Not necessarily true when you think about e.g. finding vs. verifying a solution (in terms of time complexity).

IMO verifying a solution is a great example of how reasoning is unpredictable. To say "I need to verify this solution" is to say "I do not know whether the solution is correct or not" or "I cannot predict whether the solution is correct or not without reasoning about it first".

But you will know beforehand some/a lot of properties that the solution will satisfy, which is a type of certainty.

It's not clear any of that follows at all.

Just look at inductive reasoning. Each step builds from a previous step using established facts and basic heuristics to reach a conclusion.

Such a mechanistic process allows for a great deal of "predictability" at each step or estimating likelihood that a solution is overall correct.

In fact I'd go further and posit that perfect reasoning is 100% deterministic and systematic, and instead it's creativity that is unpredictable.

Perfect reasoning, with certain assumptions, is perfectly deterministic, but that does not at all imply that it's predictable. In fact we have extremely strong evidence to the contrary (e.g. we have the halting problem).

This sounds confused. Why do you think the halting problem is relevant to predictability? Undecidable problems != Unpredictable problems

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