simple really. breakdown the word strategic and thinker. strategy means you are able to envision a plan to move towards a certain direction. Obviously, you have to be able to think this through. You also need the ability to appreciate the nuances of culture, politics and change to be a strategic thinker. This means that you need a bit of experience and maturity in your field to acquire this appreciation. Yes, an MBA will help but that's just the start. Experience, maturity and the general appreciation for the other business facets of your company (i.e, HR), will make you a better strategist.
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