You are treating a 10-month-old patient that you suspect is choking on a button. The child is responsive but apneic. After administering 5 back blows, you should immediately
Deliver 5 chest thrusts to clear the airway.
Perform a finger sweep to clear the throat of any debris.
Look in the patient's mouth with a jaw-liyaneuver.
Attempt to ventilate the infant with a bag-valve-mask.

In a 10-month-old patient suspected of choking on a button -a foreign body in the airway- conscious but apneic, after administering 5 blows to the back, you should immediately deliver 5 chest thrusts to clear the airway.

Explanation:

In a 10 month old child with airway obstruction by a foreign body, the criterion of severity indicates that it is a severe obstruction -since he is conscious but not breathing- so the sequence of actions to be taken are:

In children under one year of age, back blows and chest thrusts are intended to achieve expulsion of the foreign body by gravity or by increasing intrathoracic pressure to facilitate the release of air and force the object out, respectively.

If the infant is unconscious and the foreign body could not be removed by other measures, the airway should be explored manually to try to remove the foreign body.