A 35-year-old woman from Delhi presents with a 3-month history of persistent cough and low-grade fever. Chest X-ray shows a cavitary lesion in the right upper lobe. Sputum smear microscopy for acid-fast bacilli (AFB) is negative on two occasions. Given the high pre-test probability of tuberculosis in this clinical scenario, which investigation should be performed next to confirm the diagnosis with the highest sensitivity?