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I would just push the pawn..
Rook can not take it because of the forks of knight.
1.d6! Kf6
[1…Rxe3 2.d7 Rd3 3.d8Q+ Rxd8 4.Ne6+ Kg4 5.Nxd8+-]
2.Nd5+! Ke6 3.d7 Rh4+ 4.Kg1 Kxd7 5.g3!+- and the rook is trapped!
1. d6 {Black needs to be carful about the white knight as it can fork the king and rook or the king and d8 square, thus guarding the pawn promotion.}
1. … Rxe3
2. d7 Rd3
3. Ne6+ … 1-0