A 28-year-old woman with a 3-day history of right lower quadrant pain, fever, and vomiting presents to the hospital. On examination, she is febrile (38.8°C), has localized RLQ tenderness with guarding, and a palpable mass in the right iliac fossa. Her WBC is 16,500/μL. Ultrasound shows a dilated, thick-walled appendix with surrounding free fluid and a hypoechoic mass suggesting abscess formation. What is the most appropriate next step in management?