What should you do? Provided you and baby are doing well, I don't feel there is a need to "do" anything besides wait.
There are ways to check on how baby is doing in utero just to be sure waiting is a good option. I like using a biophysical profile to assess. A biophysical profile is an ultrasound witih additional factors measured. It measures five criteria: amniotic fluid levels, fetal movement, breathing movements, fetal heart rate, and fetal muscle tone. Each criteria is worth a maximum of 2 points. If the score is 8 or higher, that indicates baby is doing well and it is ok for the pregnancy to continue without any interventions for up to a week. I like to listen longer during prenatals to hear how baby's heart rate changes during the stimulation of palpation and how long it takes to come back down to baby's normal or resting heart rate. This helps me assess how well baby is doing. I ask clients to track baby's movements starting at 28 weeks gestation so it is easy to spot any changes that might need further evaluation. I also rely on mother's intuition since they are the ones who know baby best.
There are risks to be aware of if pregnancy goes past 42 weeks. The risk of stillbirth doubles from 1 out of 1,000 babies to 2 out of 1,000. Your baby should continue to grow so it will be larger than if you gave birth earlier. There is an increased risk of cesearean section if a hospital induction fails, meconium aspiration syndrome and baby being in the NICU.
My clients and I will have a discussion about the risks of pregnancy going beyond 42 weeks. We will also discuss the options of going to the hospital for an induction, waiting for labor to start on its own as well as gentle things that can be done at home to encourage labor to start like chiropractic or accupressure. If I do not see anything that concerns me or tells me that baby needs to come soon, and my client's intuition isn't telling her baby needs to be born, then I will support the option of waiting if that is what the client decides to do.