To become elite at strategy, you need to a) know what to do and b) have the skills required to do it

The "what do to"-part is covered under the "tool" of strategy.

But to do that, there are four key skills (with a forrest of sub-skills) required:

Analysis, to break apart a business and analyze it

Leadership, to drive processes and extract data and insights from other people

Problem solving, to break-down and get to root causes of problems and think of solutions. 

Modelling, to forecast value and evealuate  which problems to solve