What is winning strategy here?
Can't white win f pawn with Ke3-Kf4? Then White pawn majority could produce a passed pawn and win eventually.
Currently white pawns are completely safe against any king attacks. I don't see any immediate need for move a4. Move f4 would probably be bad. How could white win pawn f5 after that? Also white's own pawn cover is no longer completely impenetrable.
White to move
According to engine, a4 is best,but why?