A 65-year-old woman is evaluated in the emergency department for a 1-day history of pain and swelling in her left leg. Medical history is significant for coronary artery bypass graft surgery 8 days ago with vein harvesting from the right leg. She also has hypertension and hyperlipidemia. Medications are atorvastatin, atenolol, clopidogrel, and aspirin.

On physical examination, temperature is 37.0 °C (98.6 °F), blood pressure is 115/68 mm Hg, pulse rate is 65/min, and respiration rate is 18/min. Oxygen saturation breathing ambient air is 96%. Her sternotomy incision is healing well. The cardiopulmonary examination is normal. The left leg is swollen to the mid-thigh.

Laboratory studies reveal a hematocrit of 33%, leukocyte count of 12,000/µL (12 × 109/L), and platelet count of 55,000/µL (55 × 109/L).

Duplex ultrasonography of the left leg shows acute thrombus in the common femoral vein.

Which of the following is the most appropriate next step in management?