A method of additively manufacturing a composite part is disclosed. The method comprises depositing, via a delivery guide, a segment of a continuous flexible line along a print path. The continuous flexible line comprises a non-resin component and a thermosetting-epoxy-resin component that is partially cured. The method also comprises maintaining the thermosetting-epoxy-resin component of at least the continuous flexible line being advanced toward the print path via the delivery guide below a threshold temperature. The method further comprises delivering a predetermined or actively determined amount of curing energy to the segment of the continuous flexible line at a controlled rate while advancing the continuous flexible line toward the print path to at least partially cure the segment of the continuous flexible line.