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Why not
1. g5 Bg5 (forced, I think)
2. Rg5 Ng5
3. Qf6 Ne6 (only move)
4. Be6 and I don’t see a defense to Qg7#.
Immediately comes to mind is BxNe6 the idea to clear f8 for the queen mate.
1. Bxe6 fxe6 2. Rxe6! Rxe6 3. Rxe6 wins a pawn because if Rxe6 then white gets mated by Qf8
g5
The R nom noms, and B hits the Q.
Taking on e6 twice with rooks (not the bishop), looks like the cleanest win. At the end, white plays be6 and mate follows.
g5 doesn’t work because of Ng5.
I think Re6 is best.
RE6! 1-0