A patient presents with a painful, swollen lump on the eyelid diagnosed as a hordeolum (stye). The nurse notes no systemic signs of infection. Which intervention should the nurse prioritize to effectively treat the hordeolum and promote healing?

Apply warm compresses to the affected eyelid several times a day to facilitate drainage.

Clean the eyelid with antibacterial soap twice daily to eliminate bacteria.

Administer oral antibiotics immediately to prevent the spread of infection.

Advise the patient to wear eye patches to protect the area.