Connected and automated vehicle (CAV) technologies are likely to have significant impacts on people's travel behaviors and the performance of transportation systems. This study investigates the impacts of CAVs from various aspects, including vehicle miles traveled (VMT), emissions, and transportation equity in Southern California. A comprehensive model is developed by incorporating the supply-side improvement of CAVs, a modified activity-based demand model supported by survey data, and a multi-class highway assignment model. The simulation results showed that VMT and emissions would increase by 10%, and CAVs could worsen travel equity across income groups. To reduce the negative impacts caused by CAVs, we proposed and evaluated a series of travel demand management policies. The results indicated that all policies help to reduce the VMT and emission growth, while their performances in enhancing travel equity vary across metrics including accessibility, travel frequency, and travel distance.