[sauropod]

Actually, they do.

Broad policy is set by the administration in power and by congress.

Detailed policy and regulations implementing the broad policy goals are written by the Pentagon.

[blueplum]

I'd go one further. Broad policy is reviewed by Congress (oversight, usually after the fact)
Detailed policy and implementation - Opinions - are written by the Pentagon to present to the President
Immediate policy is set by the President

I did a quick search 'who decides foreign policy' and the 'cliffnotes' definition popped up. The bolding is their own. Note that CiC is not bolded as if it's an afterthought. One would think the sense is to emphasize the president as merely an administrative figurehead (or maybe it's just me?):
The president negotiates treaties, appoints ambassadors to represent the United States overseas, and is commander in chief of the armed forces.