A 28-year-old man with type 1 diabetes mellitus presents to the emergency department with a 3-day history of polyuria, polydipsia, and progressive lethargy. His mother reports he missed his insulin injections for 2 days due to illness. On examination, he is drowsy, respiratory rate 28/min with deep breathing, blood pressure 110/70 mmHg, and heart rate 110/min. Laboratory investigations reveal: blood glucose 450 mg/dL, arterial pH 7.25, HCO₃⁻ 12 mEq/L, PaCO₂ 28 mmHg, serum sodium 132 mEq/L, serum potassium 5.8 mEq/L, and serum osmolality 310 mOsm/kg. Urine ketones are strongly positive. What is the most appropriate immediate management step after establishing IV access and drawing blood for investigations?