A system for reducing flame holding within a combustor includes a high pressure plenum and a head end plenum defined within the combustor. A cap assembly defines an inner plenum within the combustor and a fuel nozzle passage that extends through the cap assembly. A primary fuel nozzle has an annular burner tube that at least partially defines a premix flow passage through the cap assembly. The primary fuel nozzle and the burner tube at least partially define an inlet to the premix flow passage. A high pressure flow passage and a cooling flow passage are defined within the combustor. The high pressure flow passage defines a flow path between the high pressure plenum and the inner plenum, and the cooling flow passage defines a flow path between the high pressure plenum and the head end plenum.