 Complete the following phrase:  Kennedys administration included high tensions with communist states in the Cold War. As a result, he increased the number of American military advisers in South Vietnam. The Strategic Hamlet Program began in Vietnam during his presidency. In April 1961, he authorized an attempt to overthrow the Cuban government of Fidel Castro in the failed Bay of Pigs Invasion. Kennedy authorized the Cuban Project in November 1961. He rejected Operation Northwoods plans for false flag attacks to gain approval for a war against Cuba in March 1962. However, his administration continued to plan for an invasion of Cuba in the summer of 1962. The following October, U.S. spy planes discovered Soviet missile bases had been deployed in Cuba; the resulting period of tensions, termed the Cuban Missile Crisis, nearly resulted in the breakout of a global thermonuclear conflict. He also signed the first nuclear weapons treaty in October 1963. Kennedy presided over the establishment of the Peace Corps, Alliance for Progress with Latin America, and the continuation of the Apollo program with the goal of 