A 55-year-old woman on ICU develops disseminated intravascular coagulation (DIC) secondary to septic shock from a biliary source. Her results show: platelets 35 × 10⁹/L, PT 22 seconds (control 12), fibrinogen 0.8 g/L, D-dimer >10,000 ng/mL, and she is bleeding from line sites. What is the most important management priority?