Final answer:
The initial action an EMT should take if a patient with heart problems suddenly cannot speak is to open and assess the airway, which is the first step in the BLS sequence.
Step-by-step explanation:
If a patient with a history of heart problems suddenly can't speak, the initial action for an Emergency Medical Technician (EMT) should be to C) Open and assess the airway. This is the first step in the basic life support (BLS) sequence and the airway, breathing, circulation (ABCs) approach to patient assessment. Difficulty speaking can be indicative of a stroke, and ensuring the airway is open is a critical first step in care. After assessing and managing the airway, the EMT should check for breathing and circulation and be prepared to take the appropriate actions if the patient is in distress or shows signs of a stroke.