The correct answer is E) the Square Deal.
The United States became increasingly involved in world affairs through all of the mentioned except in the Square Deal.
The Square Deal was the domestic United States program established by President Theodore Roosevelt in 1910. The main focus of the program was on taking care of US natural resources, consumer protection and the control of corporations. So the Square Deal was a national program, not a foreign affair. The foreigner affairs were the Monroe Doctrine, the Spanish-American War, the Panama Canel, the Open Door Policy, and the Roosevelt role as mediator.