(a) to ascertain who may be the putative father of such child born out of wedlock, and take appropriate steps to establish the paternity thereof in accordance with applicable provisions of law;

(b) to determine the ability and potential ability of the parents of each such child to support or to contribute to the support of such child;

(c) to take such steps and make such efforts to locate any such parent whose whereabouts are unknown to such official as all available means will allow; such means shall include, and there shall be utilization of, appropriate services offered by the department, by agencies of other states and by the federal government;

(d) to establish cooperative arrangements with the family court, county attorneys, corporation counsels and other law enforcement officials, for the establishment of paternity and location of missing parents of such children and for the enforcement of their obligations to support or contribute to support of such children to the extent of their ability;

(e) to provide pertinent information to such court and law enforcement officials to enable them to assist in locating putative fathers and deserting parents of such children, in establishing paternity and in securing support payments therefrom, provided that there is an agreement between such social services official and such court and such law enforcement officials insuring that such information will be used only for the purpose intended;

(f) to reimburse, to the extent that state and federal requirements authorize or require, appropriate courts and law enforcement officials for activities related to the requirements of this chapter and the family court act with respect to establishment of paternity and for services they have undertaken on behalf of such official.