Regarding the verification of thoughts with reason: At some point we have to trust our intuition. Gödel's incompleteness theorem states that in any system of logic, there exist true statements that cannot be proven from any finite set of axioms within the system, to say nothing of selecting axioms such that you don't arrive at any contradictory results. Sure, you can go outside the system and prove it that way, but then there's true statements that you have to go even farther out in order to prove. There are even statements, like the Riemann hypothesis, that have the curious property that if there is no way to prove that it's false, then it has to be true!
Another thing about decision making is that we don't always have the luxury of thinking carefully about a decision. Practical problems such as mental illness or deadlines can force someone to decide on something without considering every relevant thing. So the real question should be "is it ethically wrong to not put forth a good faith effort to think about a topic before acting?" and in that I would have to say, again, it depends. If you act out of ignorance or incompetence, that's fine, that leads to a learning opportunity. But if someone acts to deliberately mislead, or wishes to advance an agenda in spite of the truth (motivated reasoning), then it's ethically wrong.
There can be such a thing as overthinking a problem when faced with a practical issue, such as overcoming a trap in a dungeon. It doesn't matter if you find the optimal or intended solution, so long as you get through it. In math, however, this is not the case. When teaching how to use various mathematical techniques, it helps to attack a problem with a given technique. If you know the solution ahead of time, this serves as a check on your work during the process. This can be seen in calculus textbooks: The derivative of the power function, d/dx x^n = nx^(n-1) is first shown for n being in the set of whole numbers by using the definition of the derivative, then for rational n by using the laws of powers and logarithms, and then over the entire real number line with the assertion that every irrational number can be expressed as the limit of its decimal expansion, thus a limit of a sequence of rational numbers.
Tip jar: the author of this post has received
0.25 INK
in return for their work.