Final answer:
The nurse should immediately check the laboring woman's perineum for signs of progression in labor, indicating the baby may be ready to be born.
Step-by-step explanation:
When a laboring woman suddenly begins making grunting sounds and bearing down during a strong contraction, it suggests that she is in the active phase of labor and may be feeling the urge to push. The initial response of the nurse should be to look at her perineum for signs of increased bloody show or perineal bulging, as this could indicate that the baby is descending and getting ready to be born. It's also important for the nurse to provide reassurance, explaining that these sensations are common in late labor, and to prepare for the forthcoming potential delivery if necessary.