The Chief of Engineers may, in his discretion, modify the project for the control of floods on the Yazoo River, as authorized by paragraph (1) of this section, to substitute therefor a combined reservoir floodway and levee plan:
Provided, That the total cost thereof does not exceed the present authorization as estimated in House Committee on Flood Control Document Numbered 1, Seventy-fourth Congress, first session:
Provided further, That the modified project shall be subject to the following conditions of local cooperation:
No work shall be undertaken until the States or other qualified agencies have furnished satisfactory assurances that they will—