Final answer:
President Kennedy inspired Americans to work towards national goals by invoking patriotic duty, proposing the New Frontier legislative actions, and focusing on Cold War engagements such as the space race and the Peace Corps.
Step-by-step explanation:
President Kennedy persuaded Americans toward his goals by inspiring a sense of patriotic duty, proposing concrete legislative actions, and advocating for engagement in the Cold War era. His inaugural address, with the famous line "Ask not what your country can do for you; ask what you can do for your country," summoned the populace to contribute actively to national endeavors. Kennedy also called for active leadership and public service by recruiting talented individuals and fostering an innovative environment where progressive policies, such as the New Frontier, could thrive.
To address foreign policy and domestic challenges, he established programs like the Peace Corps and initiatives to support civil rights, education, and economic opportunities. Kennedy's commitment to winning the space race against the Soviet Union, culminating in the moon landing of 1969, demonstrated his focus on American technological leadership. Despite facing a conservative Congress, which stymied some of his domestic agenda, he managed to increase federal funds for education, raise the minimum wage, and extend unemployment insurance among others, demonstrating his leadership and legislative skills.