A 55-year-old woman is evaluated for a 3-year history of gradual left knee pain. She reports increased difficulty with stair climbing and an increase in pain over the past 6 months. She has no history of injury. She was prescribed acetaminophen, 1000 mg three times daily, and an exercise program 3 months ago but continues to have activity-limiting symptoms. Family history is notable for her mother who had a total knee replacement at the age of 65 years.

On physical examination, vital signs are normal. BMI is 31. There is bony hypertrophy of the left knee and the first metacarpophalangeal joints without warmth, erythema, swelling, or effusion.

Laboratory studies, including an erythrocyte sedimentation rate and serum creatinine, are normal.

Knee radiographs (including standing views) show medial joint-space narrowing and small osteophytes of the left knee; there is no periarticular osteopenia or marginal erosions.

Which of the following is the most appropriate next treatment?