How was nuclear war avoided?

I believe one of the reasons that the nuclear war was avoided by the good communication between the two nations. The two presidents both wrote two to three letters to each other about the resolution. They both step back and put themselves into others position. John Kennedy also presented a good leadership. He not only listened to the generals but also stood for his opinion. I believe one of the reasons of avoided the war was that the two leaders did not make wrong decisions or put themselves into bad position (wanting/starting a war). The last conference also was a important meeting. It was the time they finally had an agreement.