A 45-year-old woman presents with a 6-week history of fatigue, generalised aches, low mood, constipation, and weight gain. Examination reveals mild puffiness around the eyes and dry skin. Thyroid function tests show: TSH 15.0 mU/L (Normal 0.4-4.0), Free T4 8.0 pmol/L (Normal 12-22). What is the most appropriate management?