Final answer:
Roosevelt's statement highlights the inseparable link between the rights of independence and the responsibilities that accompany it. He advocated for a proactive presidential role and public cooperation in governance, and upheld the U.S.'s duty to ensure stability in the Western Hemisphere, as indicated by his 'big stick' foreign policy.
Step-by-step explanation:
When Franklin D. Roosevelt says, "...It's independence, must ultimately realize that the right of such independence cannot be separated from the responsibility of making good use of it.", he is conveying the message that with independence comes the responsibility to utilize that freedom effectively and justly. Roosevelt's assertion reflects his vision of governance, where the president has a proactive role to play as steward of the people, taking necessary actions for the public good as long as they are not in violation of the Constitution or laws.
In his speeches, Roosevelt emphasized the importance of public cooperation, confidence, and the correct use of the financial system to ensure the success of national programs. His foreign policy, known for the motto "speak softly and carry a big stick," was based on the belief that the United States had the right and the obligation to act as a stabilizing force in the Western Hemisphere. This view was explicitly presented in the Roosevelt Corollary, which extended the Monroe Doctrine and proclaimed the U.S. role as an international police power in Latin America.