Final answer:
The initial action should be to assess and stabilize the patient's airway and spine, ensuring the patient is breathing and preventing further spinal injury.
Step-by-step explanation:
The most appropriate initial action for the paramedics when arriving at a scene where a patient is lying at the bottom of the stairs with a facial laceration and reports pain in the hip, unable to get up, is to assess and stabilize the patient's airway and spine. This step is crucial as it helps ensure the patient is able to breathe and prevents any potential spinal injury from worsening. While administering pain medication may eventually be necessary, and a tourniquet may be required if there is severe bleeding, these actions come after the initial assessment and stabilization of vital functions. Cardiopulmonary resuscitation (CPR) is only indicated if the patient is not breathing and does not have a pulse.