Final answer:
When you find an unresponsive individual and the scene is safe, you should first simultaneously check for a pulse and breathing to quickly assess vital functions and determine if life-saving interventions are needed.
Step-by-step explanation:
When called to a home where an individual has become unresponsive, after assessing the scene to be safe, the next thing you should do is C. Simultaneously check for a pulse and breathing. This is because the immediate priority in such emergencies is to determine if the patient is in a life-threatening condition which requires urgent intervention such as cardiopulmonary resuscitation (CPR) if they are not breathing or do not have a pulse.
Other assessments such as checking blood sugar, blood pressure, and temperature, while important, come after ensuring that the patient has a viable airway, is breathing, and has circulation. Therefore, the most critical action is to quickly assess the patient's vital functions before proceeding with further medical evaluation and management.