Final answer:
If both the president and the vice president cannot serve, the Speaker of the House becomes the president, followed by the President pro tempore of the Senate as vice president, then Cabinet members in order of department establishment.
Step-by-step explanation:
In the United States, if both the president and vice president are unable to serve, the line of succession is followed to determine who would be next in line. According to the Presidential Succession Act of 1947 and the 25th Amendment, the line of succession would go to the Speaker of the House, who would become the President. The President pro tempore of the Senate would then become the Vice President. After that, the line of succession would go to the Cabinet members, in the order of their creation.
In the event that the president and the vice president cannot serve, the next in line for the presidency is the Speaker of the House of Representatives. Following the Speaker of the House, the President pro tempore of the Senate would become vice president. If the line of succession needs to be further enacted, it follows with the Cabinet members, starting with those of departments established earliest in the history of the United States. The Presidential Succession Act of 1947 and the 25th Amendment outline these procedures to ensure the continuity of government.