Doesn't that sort of invalidate the idea of making an assessment a supplemental action? If you're doing extended actions there's no initiative, thus really no such thing as those actions being supplemental or free, just how much time they take on the chart.
A supplemental action is explicitly intended for the heat of an exchange, and what good is an assessment if it doesn't model the cool intelligence of a warrior who spots his foe's weakness in the midst of a battle? Realistic or not, it is in popular culture, and it is something I think most players would expect to have modeled, so it seems to me that makes an assessment a standard/attack action...