A 58-year-old man with newly diagnosed atrial fibrillation presents with acute left leg swelling and pain. Doppler ultrasound confirms left deep vein thrombosis (DVT). PT is 12 s (normal 12–14 s), aPTT is 28 s (normal 24–36 s), and fibrinogen is 280 mg/dL (normal 200–400 mg/dL). What is the most appropriate immediate next step in management?