(a) a complete physical, psychological, and, if needed, a psychiatric examination;
(b) an investigation and consideration of family and community environment and other facts in the background of the person concerned that might relate to his delinquency;
(c) a determination of the correctional or custodial care that would be most appropriate. The Youth Services Administration shall create such facilities and employ such personnel as will enable the center to conduct the necessary physical, mental and psychological examinations required by this section.