A 72-year-old woman is admitted with febrile neutropenia 10 days after chemotherapy for breast cancer. Her temperature is 38.9 °C and absolute neutrophil count is 0.3 × 10⁹/L. Blood pressure is 108/65 mm Hg and oxygen saturation 96 percent on room air. There is no obvious source of infection. What is the most appropriate immediate management?