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Black is playing for a draw, as I see it. I would play to induce zugzwang by playing Kh7. Eventually, white will be forced to play either the king away from c4 allowing a3 and the exchange of the queenside pawns, or to move the rook hanging one of the two remaining white pawns.
if 1.. Kh7
2 h6!
the zugzwang is arrived at by Kg7!, allowing the Kh7 with the zugzwang on all that accept this ponzi scheme.
Yes, that reaches the key position 1 move earlier than I had planned.