The correct answer is the following.
You forgot to include the speech of Theodore Roosevelt. However, doing some research, we can say the following.
The philosophy that influenced America's imperialistic policy was "The United States had the responsibility to intervene in the affairs of countries deemed to be weaker and less developed."
The foreign policy developed by President Theodore Roosevelt was called "Big stick policy." It was based on the principles of the Monroe Doctrine and aimed at maintaining the US presence and control in Latin America. Under the Roosevelt administration, the US was able to use diplomacy as the first conduit to reach an agreement but never hesitate to use the force of the military.