Final answer:
Upon the President's death, the Vice President becomes the President. If the Vice President is unable to serve, the Speaker of the House is next in line, followed by the President pro tempore of the Senate and then the Secretary of State, as per the 25th Amendment.
Step-by-step explanation:
In the event the President of the United States dies, the proper order of presidential succession is as follows: firstly, the Vice President takes over. If the Vice President is unable to serve, then the Speaker of the House of Representatives is next in line. In an instance where both the President and Vice President are unable to serve, the Speaker would take over as President and the President pro tempore of the Senate would become Vice President, as stated in the Presidential Succession Act. Following this, the line of succession continues to Cabinet members, beginning with the Secretary of State.
This order is delineated in the 25th Amendment of the U.S. Constitution, which also provides procedures for dealing with vacancies in the office of the President and Vice President. It clarifies that the Vice President shall assume the presidency upon the death, resignation, or removal of the sitting President. Moreover, if the Vice President's office becomes vacant, the President can nominate a candidate who then must be confirmed by a majority of both Houses of Congress. The 25th Amendment ensures the continuity of government and a clear line of succession.