Any county may participate in an intergovernmental agreement under this Act notwithstanding the absence of specific authority under State law to perform the action involved provided that the unit of local government contracting with the county has authority to perform the action. The authority of the county shall be limited to the territorial limits of the local governmental unit with which the county contracts. In the case of an intergovernmental agreement between a county and a municipality, however, the agreement may provide that the county may perform an action within the territorial limits of the municipality, within the contiguous territory not more than one and one-half miles beyond the corporate limits and not included in any municipality, or within both.