Avictim with a foreign-body airway obstruction becomes unresponsive. what is your first course of action

The answer to this question would be: start doing CPR.

If the victim becomes unresponsive, probably the foreign body completely obstructs the airway and the oxygen level is already too low. Without the victim help, taking out the foreign body will be hard.
In this case, CPR will be the best option since the pressure from chest might push the foreign body away and the CPR can help circulate the blood.