After the work is done and the actual cost is known, the council shall decide whether the property benefited shall bear all or a portion of the total cost. The City Engineer shall prepare the proposed assessment for all property within the assessment district. The proposed assessment shall be approved by council. Notice of the proposed assessment shall be mailed to the owner of each property to be assessed. Each notice shall state the amount of assessment proposed on that property and the date by which objections must be filed with the city manager. All objections shall be in writing and state the grounds of the objections.