A 58-year-old male smoker with COPD presents with dyspnea and cyanosis. Arterial blood gas shows pH 7.32, PaCO₂ 58 mmHg, HCO₃⁻ 28 mEq/L, PaO₂ 52 mmHg. To assess the primary mechanism of hypoxemia and guide therapy, which investigation is most appropriate?

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