Final answer:
When a newborn remains apneic and cyanotic after initial resuscitation steps, ventilations with a bag-valve-mask should be started. This action provides necessary oxygen and stimulates breathing.
Step-by-step explanation:
If a newborn remains apneic and cyanotic following the initial steps of resuscitation, the correct course of action is B) begin ventilations with a bag-valve-mask. This intervention is indicated when a baby is not breathing or the breathing is insufficient after birth. It helps to deliver oxygen and stimulate the baby's respiratory drive. The use of a bag-valve-mask should be started promptly according to the neonatal resuscitation guidelines if improvement with initial steps is not observed. Only if the heart rate is found to be less than 60 beats per minute after 30 seconds of proper ventilation should chest compressions be initiated. The Apgar score, which assesses heart rate and respiration among other signs, is critical in determining the condition of the newborn and the need for resuscitation.