Degeneracies in multilayer graphene, including spin, valley, and layer degrees of freedom, can be lifted by Coulomb interactions, resulting in rich broken-symmetry states. Here, we report a ferromagnetic state in charge-neutral ABCA-tetralayer graphene driven by proximity-induced spin-orbit coupling from adjacent tungsten diselenide. The ferromagnetic state is identified as a Chern insulator with a Chern number of 4; its maximum Hall resistance reaches 78% quantization at zero magnetic field and is fully quantized at either 0.4 or -1.5 tesla. Three distinct broken-symmetry insulating states, layer-antiferromagnet, Chern insulator, and layer-polarized insulator, along with their transitions, can be continuously tuned by the vertical displacement field. In this system, the magnetic order of the Chern insulator can be switched by three knobs, including magnetic field, electrical doping, and vertical displacement field.