During labor, what is the most important intervention after membranes have ruptured?

After the membranes have ruptured during labor, assessing for a change in fetal heart rate is the most important intervention. The rupture of membranes can increase the risk of cord prolapse or other complications that might affect fetal oxygenation. Thus, continuous monitoring of the fetal heart rate is critical to ensure that the fetus is tolerating labor well. A change in fetal heart rate can indicate distress, prompting the healthcare provider to take necessary actions to address any issues that may arise, such as repositioning the mother or providing additional interventions.

The other choices serve different purposes in monitoring maternal and fetal health but are not as immediate or critical in this specific situation following the rupture of membranes. Checking for protein in urine is more related to assessing for preeclampsia, monitoring blood pressure helps track maternal health, and encouraging deep breathing exercises can aid in relaxation but does not directly assess fetal well-being.