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".
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).