Correlated equilibrium proved by convexity (Games Theory)

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I am finding very hard to understand how convexity works and why a correlated strategy if a convex linear combination of Nashes is a correlated equilibrium. (Both concepts of Correlated strat. and correlated equilibrium are clear)

The following is the problem I can't grasp: problem

Please feel free to modify my post I haven't been posting in a while and writing LateX feels very hard, also the question isn't well posed but I am trying to solve this on my own and this post is just another attempt to find a solution

Thanks to anyone helping