Final answer:
The Teller Amendment was the pivotal U.S. government action that protected Cuba from annexation by explicitly stating that the United States had no intention to control Cuba after the Spanish-American War. It was integral in establishing the U.S. policy towards Cuba, leading to the Platt Amendment and the lease of Guantanamo Bay.
Step-by-step explanation:
The government action that protected Cuba from being annexed was the Teller Amendment. The Teller Amendment was passed by Congress as a part of the declaration of war against Spain, which resulted in the Spanish-American War. It was an effort to alleviate concerns over American imperialistic intentions by officially renouncing any American control over Cuba after the war. The declaration promised to assist Cubans in securing independence from Spain and specified that the United States would not annex Cuba. The Amendment played a crucial role in setting the principles under which the United States would later engage with Cuba, influencing later actions like the inclusion of the Platt Amendment in the Cuban Constitution, which allowed for U.S. intervention to preserve Cuban independence and led to the lease of the Guantanamo Naval Base to the United States.