What action should you take for a 2-year-old child who suddenly appears cyanotic and cannot speak after playing with a small toy?

In the scenario described, the child is likely experiencing a choking episode due to a foreign body obstruction in the airway, as indicated by the sudden onset of cyanosis and inability to speak. In such cases, the priority is to clear the airway and restore normal breathing.

Performing abdominal thrusts, often referred to as the Heimlich maneuver, is the appropriate response for children over the age of one who are choking. This technique involves applying upward pressure under the diaphragm, which can help to expel the obstruction from the airway. It is important to apply the thrusts carefully, as the child is only two years old, and the force applied should be appropriate to their size and body structure.

The other options would not address the immediate need to remove the obstruction effectively. Back blows can be part of the response, particularly for infants, but in this case, the child's age indicates that abdominal thrusts should be prioritized. Starting chest compressions is not suitable in this scenario as it does not address the airway obstruction. Providing oxygen is also not an immediate solution since the priority is to ensure the airway is clear before any other measures can be effective. Therefore, performing abdominal thrusts is the best course of action to resolve the choking situation.