A 42-year-old man with a family history of medullary thyroid carcinoma presents to the emergency department with acute severe headache, chest tightness, and blood pressure 210/130 mmHg. His 24-hour urine metanephrines are markedly elevated at 8.5 nmol/L. Abdominal imaging reveals bilateral adrenal masses (2.5 cm left, 1.8 cm right). Serum calcium is 10.2 mg/dL (normal 8.5–10.5). What is the most likely underlying genetic syndrome, and what is the recommended screening for this patient's first-degree relatives?