(5) Educational service agency.--The term `educational service agency'--
(A) means a regional public multiservice agency--
(i) authorized by State law to develop, manage, and provide services or programs to local educational agencies; and
(ii) recognized as an administrative agency for purposes of the provision of special education and related services provided within public elementary schools and secondary schools of the State; and
(B) includes any other public institution or agency having administrative control and direction over a public elementary school or secondary school.