The word strictly is ambiguous because it could mean "sternly" or "only." I am guessing that you mean "sternly."
You could probably say, "In the US, police have begun to take strict action." Another option might be "In the US, police have reacted with firm and decisive action."
In this sentence, you could probably place "in the US" in a few different places without readers misreading the meaning because police generally stay in their own country and, therefore, it is unlikely that a reader would interpret the meaning as police from another country acting in the US. Still, I think it is a good exercise to think about prepositional phrases and how their placement can affect the meaning (or potential interpretation) of a sentence.
Finally, although the sentence is grammatically complete, the idea might sound more complete if you named one or more of the actions taken. If the surrounding context clarifies the idea, then no further information is needed.