Rook endgame question
OK what I do now is I look at some of my old games and try to play them against Fritz, and play better than I did in the actual game so I can see how I should have won...in one of those games I am at a point where I reached a rook endgame, it's in the diagram below. I'm Black and it's my move. I should be winning but I want to clearly know HOW.To all of you endgame experts- which is the correct option- play my rook to a5 to protect the a4 pawn and push my kingside pawns, or should I play Rc3, win his h-pawn, let him take my a-pawn, put my rook on the a-file behind his pawn and push my 3 connected passed pawns on the kingside? Which is the correct procedure and WHY ? Tell me step by step what I should do...thanks very much.