A 64-year-old woman on chemotherapy for breast cancer presents with a temperature of 38.5°C and rigors. She is day 10 after her last cycle. Her neutrophil count is 0.4 × 10⁹/L. Blood pressure is 110/70 mmHg and heart rate 105 beats/min. According to febrile neutropenia guidelines, which is the most appropriate immediate management?