I offer a POV that is in the middle: reasoning is powerful to evaluate which solution is better among N in the context. Memorization allows sampling of many competing ideas from the problem space, than the LLM picks the best, making chain of thoughts so effective. Of course zero shot reasoning also is a part of the story but somewhat weaker, exactly like we are not often able to spit the best solution before evaluation of the space (unless we are very accustomed to the specific problem).