I work the same way. But you have to be careful... My first reaction when I'm faced with a tricky problem is to sit there and think about it for a few minutes, rather than jump to action (with possible disastrous results). But it can make you look kind of dumb, just sitting there staring blankly in the face of a problem.
In the long run though, people have learnt to trust me, since that couple minutes of thinking often leads to great results.
I do something else while my subconscious works. Careful: 15 minutes on HN is good; an hour is procrastination.