Final answer:
The nurse's first action should be to massage the fundus and give an oxytocin agent to promote uterine contractions and prevent postpartum hemorrhage, which is a priority following delivery.
Step-by-step explanation:
Upon a woman's arrival at the labor and delivery unit after delivering her infant and the placenta, the priority is to ensure her ongoing safety and the well-being of her newborn. The first action the nurse should take is to massage the fundus and give an oxytocin agent. Fundal massage promotes uterine contractions to prevent hemorrhage by compressing the blood vessels and minimizing blood loss. Additionally, oxytocin augments the contractions to further lessen the risk of postpartum hemorrhage. Checking the perineum for lacerations, collecting specimens for hemoglobin and hematocrit, and placing the infant to the breast for bonding are important but follow the immediate need to prevent bleeding.