The Cuban missile crisis proves that the 'cooler heads prevailed' as the conflict did not escalate.
Explanation: The Cuban missile crisis was the closest that the world ever got to a full-blown world war with nuclear weapons and it was the heads that were cool and composed during these times of frenzy that saved the two nations.
By the end of the crisis, it was understood that both sides did not want the conflict and would rely on the doctrine of mutually assured destruction to not escalate future conflicts.
Thus, the end shows that, in fact, cooler heads prevailed at the time.
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