If both the president and the vice president can no longer serve, who will be proclaimed the next leader of the country?

The Speaker of the House of the United States (provided your question is about the United States) will be the next leader of the country.

Explanation:

The United States Presidential Succession Act of 1947 is the latest law defining the line of succession for the position of President of the United States. In fact, Section a (1) states:

(a)

(1) if, by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President to discharge the powers and duties of the office of President, then the Speaker of the House of Representatives shall, upon his resignation as Speaker and as Representative in Congress, act as President.

The Speaker would then be followed by the President Pro Tempore of the Senate, and then go down the ranks of the Presidential cabinet.