; (F) will be publicly administered by an agency of the State; (G) will not preclude the purchase of supplemental insurance; (H) will provide systems for complaints, appeals, independent review, and other procedures for accessing and maintaining benefits that are at least as accessible to State residents as those of the specified Federal health programs (as defined in subsection (i)(4)) for which such residents would have otherwise been eligible without application of such waiver under subsection (a)(1)