Habit #7 (box 10), Sharpen the Saw is quite unlike the six earlier habits. How to make improve your skills and abilities in the first six habits is the purpose of Habit #7.
All virtuous cycles eventually reach limits of growth. This is a basic truth about reinforcing loops. Box 10 or Habit #7 is the secret of how to exceed the natural limits of growth. Any effective and successful person practising the first six habits would have on their own eventually realize they have to sharpen their saw.
The first three habits are foundational to the entire 7 Habit system. Note that there is no promotion arrow going from the virtuous cycle consisting of box 3,4 and 5 but it receives from box 6.
What is missing from Covey's book is how to sharpen your saw. He has left that to us.