What is the strongest continuation for White?

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Analysis of john2001plus (1958) vs. aherring74 (1931)

8 7 6 5 4 3 2 1 a b c d e f g h +1

(white to move) 1. Nf3 f5 2. e4 fxe4 3. Ng5 Nc6 4. d3 e3 5. Bxe3 e5 6. c4 Nf6 7. Nc3 Bb4 8. Be2 O-O 9. O-O Nd4 10. Bxd4 exd4 11. Nce4 Nxe4 12. Nxe4 d5 13. a3 Be7 14. cxd5 Qxd5 15. Bf3 Qf5 16. Re1 Qf7 17. Rc1 c6 18. Qa4 Rd8 19. Rc4 b5 20. Qa5 bxc4 21. dxc4 Be6 22. Nc5 Bxc4 23. Bxc6 Rac8 24. Nb7 Rf8 25. Bf3 g5 26. Qe5 Bf6 27. Qg3 Qc7 28. Nd6 Bb3 29. Nxc8 Qxg3 30. Ne7+ Bxe7 31. hxg3 Bf6 32. Be4 Rc8 33. Bf5 Rc7 34. f4 Bc4 35. Rc1 Bd8 36. Rxc4 Rxc4 37. Be6+ Kg7 38. Bxc4 Kf6 39. Bd3 h5 40. Kf2 Bb6 41. Kf3 g4+ 42. Ke4 Ke6 43. b4 Kf6 44. a4 Bc7 45. a5 Ke6 46. Bc4+ Ke7 47. Kf5 d3 48. Bxd3 Kd6 49. Kg5 Kd5 50. a6 Kd4 51. Bf1 Ke3 52. Kxh5 Kf2 53. Kxg4 Kxf1 54. Kf3 Bb6 55. g4 Bd4 56. g5

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