I think my most valuable skill is my ability to build models of problems and systems. Not necessarily great and complete models, but at least something that encapsulates a bit of what seems to be going on and produces output that can be compared with the system. A few iterations of modelling/comparison/correction and I have usually at least learned something useful. It works both for napkin calculations or software simulations. It is a great tool for understanding many systems or checking intuitions.

Others have mentioned the skill of "letting go". I have trained myself the speciality of letting go of negative emotions, which has produced a very sunny (nearly pathologically positive) mood. Recognizing that most negative emotions like despair, sadness or anger don't solve the problem that caused them is very helpful. A positive, can-do mindset is a pretty useful asset. However, there are tricky trade-offs to be made between lowered ability to dwell on negatives plus optimism bias and the hedonic enjoyment of a good mood.