Sec. 4. If:
(1) public assistance has been furnished for the child by the division of family resources; and
(2) an assignment of support rights under Title IV-D of the federal Social Security Act (42 U.S.C. 651 through 669) has been executed on behalf of the child;
the division of family resources or the county office of family and children may file an action before the child becomes nineteen (19) years of age or graduates from high school, whichever occurs first.