A 3-year-old girl is referred to the pediatric ophthalmology clinic for evaluation of bilateral leukocoria detected during school screening. Fundoscopy reveals multiple white retinal masses in both eyes, with the right eye showing larger lesions and vitreous haze, while the left eye has smaller, more peripheral lesions without vitreous involvement. B-scan ultrasonography and MRI confirm bilateral retinoblastoma with no evidence of optic nerve involvement or extraocular extension. Systemic staging (chest CT, bone marrow biopsy) is negative for metastases. The child's parents are unaffected, and there is no family history of retinoblastoma. What is the most appropriate initial treatment strategy for this child?