A 6-month-old infant presents with a fever of 39.2°C, irritability, and poor feeding for 12 hours. On examination, the baby appears listless, has a capillary refill time of 3 seconds, heart rate 180 bpm, and respiratory rate 55/min. There are no specific focal signs of infection. According to NICE NG51 (Sepsis), what is the most immediate action required?