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How could I detect if a notebook is currently the active window?

This is what I have tried, but it does not work as the value of x is never updated:

EventHandler[ CreateDocument[ {TextCell["Window status:", "Text"], ExpressionCell[Dynamic[x], "Output"]}], {"FocusGained" :> (x = "This window is active"), "FocusLost" :> (x = "This window is not active")}]

UPDATE: With the help of Carl's answer, I would like to share the motivation for the question. Without the Enable part, using the FileNameSetter (without making the window active first) would produce a "INTERNAL SELF-TEST ERROR: winModality|c|511" (CASE:4033279). Now I can avoid it:

CreateDocument[{ExpressionCell[ Dynamic[ FileNameSetter[Dynamic[f], Enabled -> SelectedNotebook[] === EvaluationNotebook[]]], "Output"]}, WindowSelected -> False]
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You could try something like:

CreateDocument[{ TextCell["Window status:", "Text"], ExpressionCell[ Dynamic[SelectedNotebook[]===EvaluationNotebook[], UpdateInterval->1], "Output" ] }]

Here's an animation:

enter image description here

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    $\begingroup$ Might be more convenient in the NotebookDynamicExpression. Or bound to the MouseEntered and MouseExited events. $\endgroup$ Commented Jun 7, 2018 at 0:10

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