A 7-year-old boy is brought to the emergency department after a fall on an outstretched hand (FOOSH) while playing in school. He presents with severe pain, swelling, and deformity of the left elbow. On examination, the elbow is held in flexion, and there is gross swelling. Neurovascular examination reveals absent radial pulse, but the hand is warm and pink. X-ray confirms a displaced supracondylar fracture of the humerus (Gartland Type III). What is the most appropriate immediate management?