Final answer:
Cuba allowed the United States to set up a naval base at Guantánamo Bay, to intervene to preserve its independence, and to intervene to maintain a stable government, as per the Platt Amendment.
Step-by-step explanation:
The actions that Cuba allowed the United States to take are clearly defined by the historical context of the Platt Amendment. Firstly, Cuba consented to the United States setting up a naval base, particularly at Guantánamo Bay. Secondly, the Platt Amendment granted the United States the right to intervene to preserve Cuba's independence, which was a pivotal element in the amendment. Thirdly, it enabled the United States to intervene to maintain governmental stability, ensuring that foreign powers did not interfere with Cuba's newly found sovereignty. These conditions greatly shaped the Cuban government and its relations with the United States during the early 20th century.