A 28-year-old woman with type 1 diabetes mellitus presents to the emergency department with a 2-day history of polyuria, polydipsia, and progressive lethargy. She admits to missing insulin injections for 3 days. On examination, she is tachypneic (RR 28/min), blood pressure 110/70 mmHg, and has fruity-smelling breath. Laboratory investigations reveal: blood glucose 580 mg/dL, arterial pH 7.18, HCO₃⁻ 12 mEq/L, and serum ketones strongly positive. Which of the following best explains the biochemical mechanism underlying the elevated ketone bodies in this patient?