A 35-year-old woman is brought to the emergency department by emergency medical services after sustaining multiple injuries during a high-impact motor vehicle collision. She was found unresponsive at the scene, with significant facial contusions and an obvious deformity of her right forearm. Her Glasgow Coma Scale (GCS) is assessed at 6. Initial vital signs upon arrival are: temperature 37.20C, blood pressure 88/50 mmHg, heart rate 124 beats/min, respiratory rate 5 breaths/min, and oxygen saturation 88% on a non-rebreather mask. Her breathing is shallow and gasping, with noted paradoxical movement of the left chest wall. She has clear signs of significant ecchymosis over the chest and abdomen. There is no obvious external hemorrhage. She is able to be bag-mask ventilated with significant resistance. Considering the patient's presentation, what is the most critical immediate diagnostic and therapeutic intervention to stabilize her condition?