A 28-year-old man with known HIV infection (CD4 count 150 cells/μL) presents with fever, cough, and dyspnea. Sputum smear microscopy is negative. A rapid molecular test (Xpert MTB/RIF) on sputum is positive for *M. tuberculosis* with no rifampicin resistance detected. Which investigation should be performed next to assess for drug-resistant TB and guide second-line therapy?