A 32-year-old woman from Delhi presents to the emergency department with acute onset fever, severe headache, and neck stiffness for 6 hours. CSF is obtained via lumbar puncture and sent for analysis. On Gram stain of the CSF, gram-negative diplococci are seen. The CSF shows 450 WBC/μL (90% neutrophils), protein 180 mg/dL, and glucose 25 mg/dL (serum glucose 120 mg/dL). What is the most appropriate immediate next step?