Whenever a portion of a district equal to at least sixty percent of the area or sixty percent of the assessed valuation of the real property lying within such district, is included within the corporate boundaries of a city, the city may assume by ordinance the full and complete management and control of that portion of the entire district not included within another city, whereupon the provisions of RCW
35.13A.020 shall be operative; or the city may proceed directly under the provisions of RCW
35.13A.050.