A system for additively manufacturing a composite part is disclosed. The system comprises a housing and a nozzle. The nozzle is supported by the housing. The nozzle comprises an outlet, sized to dispense a continuous flexible line. The continuous flexible line comprises a non-resin component and a photopolymer-resin component. The system also comprises a feed mechanism, supported within the housing. The feed mechanism is configured to push the continuous flexible line out of the outlet of the nozzle. The system further comprises a light source, supported by the housing. The light source is configured to deliver a light beam to the continuous flexible line after the continuous flexible line exits the outlet of the nozzle to at least partially cure the photopolymer-resin component of the continuous flexible line.