The Two Way Thought Process

Sometimes while solving a problem, I have discovered for myself that the discovery works two ways

1. If a small problem is solved, one can generalize the solution and it becomes a learning
2. If a generic problem is solved, one can apply it to niche areas and problems to solve complex problems

Usually, I keep oscillating between (1) and (2). However, I wonder whether one should apply (1) or (2) to a problem first? I suspect it should be (1) and the authors of Concrete Mathematics seem to agree. What do you think?