A 28-year-old woman presents to the gynecology clinic with a 5-day history of purulent urethral discharge and dysuria. She is sexually active with a new partner. Gram stain of urethral exudate shows Gram-negative intracellular diplococci within neutrophils. Culture on Thayer-Martin medium yields oxidase-positive colonies. Nucleic acid amplification test (NAAT) confirms the diagnosis. What is the most appropriate first-line treatment for this patient?