The Mayor of the City, in addition to duties prescribed elsewhere in this Charter, including acting as presiding officer at Council meetings and voting in case of a tie, shall from time to time communicate to the City Council such information and recommendations as may, in his or her judgment, tend to the improvement of the finances, police, health, comfort, and good government of the City. He or she shall represent the city in all its relations with other municipalities, and with the state, and the United States, and he or she shall perform such other duties and exercise such other powers not inconsistent with the provisions of this Charter and the Constitution of the State of Texas and all laws relative to mayors of home rule cities, and the Constitution and statutes of the State of Texas.