Are you being deliberately obtuse? The number of around 1000 US foreign military bases is well collaborated, even by US professors and researchers. The existence of organisations like AFRICOM and US foreign troop deployments to countries like Germany and South Korea is well known. It’s not a matter of belief.
But they usually always do, because of the implication…
You are aware that the US and UK were not the only countries to deploy troops to Iraq (not Iran, as you mistakenly claim). There was a whole NATO training operation involving 13 NATO member states. 20 of the current 31 NATO members had some form of troop deployment in Iraq between 2003 and 2011.
I am not American, and it’s quite clear the US does use it’s military might when it needs to, to dictate the order of the world, and there is nothing that the EU can do about it. Precisely because their sovereignty is curtailed due to being US vassal states. Of which NATO membership is a key part. This includes actions against the EU. Unless you want to argue that the nordstream gas pipelines just spontaneously combusted.