The Soviet Union wouldn't invade Europe or the western hemisphere and the US wouldn't invade Cuba or Turkey
President Kennedy demanded that the Soviet Union remove the missile base from Cuba. He also ordered a US air and naval blockade of Cuba to prevent Soviet arms shipments from reaching Cuba. He prepared to invade Cuba in case Khrushchev did not withdraw his missiles. He made an agreement with Khrushchev at the last minute: Khrushchev agreed to remove the missiles from Cuba, ordered his ships to turn back to Soviet Union; Kennedy promised not to put missiles in Turkey, near the Soviet border. After this agreement Kennedy lifted the blockade and promised not to invade Cuba.
President Kennedy set up a naval blockade to turn back Soviet ships that were carrying missiles to Cuba. The US promised not to invade Cuba and to remove nuclear missiles from Turkey and Europe in exchange for the dismantling of missile bases in Cuba. The US claimed, that it had already planned the Turkey missile bases.
The US recruited Cuban exiles to invade the Bay of Pigs in Cuba in 1961 in an attempt to overthrow Fidel Castro's government. The invasion was ultimately unsuccessful and tarnished the reputation of President Kennedy.
President Kennedy set up a naval blockade to turn back Soviet ships that were carrying missiles to Cuba. The US promised not to invade Cuba and to remove nuclear missiles from Turkey and Europe in exchange for the dismantling of missile bases in Cuba. The US claimed, that it had already planned the Turkey missile bases.
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JFK kickstarted the project to go to the Moon, tried to invade Cuba (the Bay of Pigs), and proved that 1960s security was not strong enough, among other things.
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He couldn't do that because the missiles were Russian in Cuba. Cuba was being used by the Russians and if he had invaded there would have been a war. In fact, it got within hours of war before an agreement was reached to remove the missiles. So, it wasn't as easy as invading Cuba and causing a war between two superpowers.
A naval blockade of the island of Cuba (or Cuber as Kennedy used to pronounce it).