Question about AutoAction (or Mouseover)

The code below creates an ActionMenu that opens when I mouse over it. This is what I want… however, I would like it to close the ActionMenu when I move the mouse away from the ActionMenu. I cannot get it to work. It forces me to click somewhere to remove the ActionMenu. Can anyone help?

Thank you in advance!
Mike

ActionMenu["Boxes",
 {"Definition" :> {SelectionMove[InputNotebook[], After, Cell]},
  "Theorem" :> {SelectionMove[InputNotebook[], After, Cell]},
  "Procedure" :> {SelectionMove[InputNotebook[], After, Cell]},
  "Example" :> {SelectionMove[InputNotebook[], After, Cell]}
    }, Appearance -> "PopupMenu", AutoAction -> True]
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