A carbon reduction assembly adapted for use with wet and dry coal combustion products (“CCPs”). The assembly includes a direct-fired carbon reduction section having a dry material inlet device that is adapted to receive the dry CCPs and a direct-fired carbon reduction section burner unit that is adapted to reduce carbon content in the dry CCPs. The assembly also includes a direct-fired dryer section that is operatively connected with the direct-fired carbon reduction section and has a wet material inlet device that is adapted to receive the wet CCPs and a direct-fired dryer section drum that is adapted to dry the wet CCPs. The assembly further includes a control unit that is operatively connected with the carbon reduction section and the dryer section. An amount of hot gas generated by the carbon reduction section is conveyed to the dryer section, and the assembly is adapted to produce dry fly ash.