Final answer:
The Big Stick diplomacy, associated with President Theodore Roosevelt, is the diplomatic style that most promoted military action as it relied on the threat of military force to achieve foreign policy objectives.
Step-by-step explanation:
The diplomatic style that most promoted military action was the Big Stick diplomacy. This approach was championed by President Theodore Roosevelt, who believed that the threat of military force was effective in achieving foreign policy goals without actually engaging in conflict. Roosevelt's Big Stick policy aimed to project American power and influence globally, though he intended to use the military as a deterrent rather than engaging in continuous warfare. The legacy of this policy is rooted in the axiom, "Speak softly, and carry a big stick, and you will go far," emphasizing the strategic use of military might as a way of negotiation. In contrast, President William Taft's Dollar Diplomacy focused on using economic power to influence foreign affairs, resorting to military action when economic coercion failed.