But the real trick is that after you complete the important and urgent tasks, you should move to complete the important and not urgent tasks.

This is definitely a step up from working on non-important tasks, but for more clarity and nuance on the issue I'd recommend reading The Seven Habits of Highly Effective People. The author, Stephen Covey, argues that important and non-urgent tasks are consistently under-emphasized compared to the important and urgent tasks. That kind of mindset leads to putting out the fires all the time, rather than dealing with things pro-actively and not having the fires in the first place.