In addition to all authority previously granted by statute, city boards of education may enter into cooperative agreements, projects and programs with the city council or commission, and may take such other actions as they deem necessary and appropriate for the proper management of the public schools; provided, however, that such agreements, projects, and programs shall not be in conflict with nor inconsistent with any law or policy of the State Board of Education and shall not conflict with the purposes for which the school system is established. Provided, further, that such authority shall not be used to deny any employee any legal or constitutional rights to which he or she is entitled, nor shall such authority be used in such a way that employees are denied any benefits established and required by law, nor shall such authority be construed as authorizing city boards of education to levy any taxes not otherwise authorized by law.