What should you do if a choking person is coughing forcefully?

When a choking person is coughing forcefully, allowing them to continue coughing is appropriate because it indicates that they have some airway obstruction but are still able to breathe and effectively generate airflow. Coughing is a natural reflex that can help expel the object causing the obstruction, and it's a sign that the person is still partially able to manage their airway on their own.

Encouraging the person to keep coughing allows their body to work towards dislodging the object without the need for more invasive procedures. Taking actions such as abdominal thrusts, chest thrusts, or CPR would be unnecessary and potentially harmful at this stage, as those procedures are designed for situations where the person cannot cough, speak, or breathe effectively. Thus, letting them try to cough up the obstruction is the best immediate response in this scenario.