A 25-year-old woman presents with fatigue, weight gain, and cold intolerance. On examination, she has a non-tender, diffusely enlarged thyroid gland. Laboratory studies reveal elevated TSH and low free T4. A radionuclide thyroid uptake study shows normal uptake of radioactive iodide at 1 hour. However, when perchlorate is administered, 35% of the trapped iodide is discharged from the thyroid gland. Which step in thyroid hormone synthesis is most likely defective in this patient?