A 30-year-old Somali refugee newly arrived in the UK is found to have a productive cough, night sweats, and weight loss. Chest X-ray shows upper lobe cavitation. Three sputum samples are sent. The first Ziehl-Neelsen stain shows acid-fast bacilli. GeneXpert MTB/RIF is positive for Mycobacterium tuberculosis with rifampicin resistance detected. What is the most appropriate initial management?