The hidden patterns of logic

In the previous post I mentioned certain ommisions in my pattern database, mainly in the endgame. My main goal is to learn to apply logic to the chessgame, I might as well combine this with endgames. Mr. Z gave me a quite interesting position:

.
.
.
.
Black to move.
This is a win for black, but it is easy to go astray when you play this out against a chess engine. Can we find the moves by applying logic?

What is going on in the position?
If you think away the rooks, the remaining pawn endgame is an easy win for black. Black has a pawn more at the kingside, which he has to transform into a passer. When white takes the passer with his king, black can eat away the white pawns on the queenside. So white has to avoid the exchange of rooks. This limits the freedom of move of the white rook a bit.

The natural targets are the bases of the pawn chains, i.e. h7, b7, a7 and g2, c3, a3.
The natural attackers are the rooks.
The kings have to prevent the invasion of the rooks.

There is only one open line which is easy to control by black. White has to seek counter attack by opening an extra line on the queenside. That is a slow plan, since it involves at least two pawn moves (a4, b5 for intance) and 3 rookmoves (Rd3, Rd1, Rb1 for instance). Blacks natural plan is to create a passer on the kingside. This means he must move the pawns h7 and g6 forward. He need his king to support that.

It is always good to make a move that serves more than one goal. If you can serve more goals then your enemy, you havemore chance to reach one of your goals.
1. ... Kf7 is such move:

• It defends g6, thus freeing h7.
• It defends the invasion squares e8, e7 and e6. Thus relieving the rook from a defensive task.
• The king is one move closer to the queenside, where he might be needed for defense.

White can play 2.Rd3 for instance, according to his plan.

.
.
.
.
Black has now several moves that all serve the same goal: creating a passer on the kingside.
For instance h5, g5 or Re4+ (to make room for f4). Re4+ has the additional advantage that the rook can help in the defense when white brakes through at the queenside.