Behçet disease and recurrent uveitis

A 42-year-old woman presents with recurrent episodes of anterior uveitis over the past 18 months. Slit-lamp examination reveals fine keratic precipitates and posterior synechiae. Systemic workup including chest imaging, ACE level, and syphilis serology are all negative. On review of systems, she reports recent onset of painful oral ulcers and genital ulceration. Which of the following is the most likely diagnosis?