A 38-year-old man from Delhi presents to the emergency department with a 3-day history of severe right knee pain, swelling, and inability to bear weight. He has a fever of 38.9°C and reports a small puncture wound to the knee sustained while gardening 5 days ago. On examination, the knee is warm, erythematous, and grossly swollen with severe pain on passive movement. Synovial fluid analysis shows WBC 85,000/μL (95% neutrophils), protein 6.2 g/dL, glucose 18 mg/dL (serum glucose 110 mg/dL), and negative Gram stain. Blood cultures are pending. What is the most appropriate next step in management?