How can you choose the tool of problem solving?

That depends on the root causes of the subject problem. For example dealing with manpower problems require tools different to those used to deal with funding issues.

It all depends on the approach. My approach is finding the gap first and using a braod view to see how it affects around. Then I jot down possible needs that are required to control the problem. Once I'm done with that I advance to solutions to all these needs with my target as problem diminution. It's very simple once you get to it. Just like a show casting, where thousands of people are auditioned and only one is chosen, it has to be out there and satisfying.