A 62-year-old woman presents with a 6-month history of pain and stiffness in her hands, particularly affecting the metacarpophalangeal (MCP) and proximal interphalangeal (PIP) joints bilaterally. The stiffness is worse in the mornings and lasts for over an hour. On examination, there is swelling and tenderness of these joints. Blood tests show a raised ESR and positive rheumatoid factor. What is the most likely diagnosis?