The legislature shall provide for the assessment by the state of the property of those public service businesses assessed by the state at the date this constitution becomes effective, and of other property as designated by the legislature, and for the imposition and collection of taxes thereon. Property assessed by the state shall be assessed at the same proportion of its true cash value as the legislature shall specify for property subject to general ad valorem taxation. The rate of taxation on such property shall be the average rate levied upon other commercial, industrial, and utility property in this state under the general ad valorem tax law, or, if the legislature provides, the rate of tax applicable to the property of each business enterprise assessed by the state shall be the average rate of ad valorem taxation levied upon other commercial, industrial, and utility property in all counties in which any of such property is situated.