You can speak with your doctor/gynae. Previously I was at NUH, subsidy route I was allowed to go till 41 weeks. I give birth the next day. For KKH I wasn't allowed. I did till 40 weeks and give birth 2 days later. If you can extend go for it and chances of second birth no induce is there. You can ask them to check if the cervix has opened. Most of the time, not all Mummies will have their cervix dilate pretty fast when you have a sign of birth. My #2 I was supposed to be induced but didn't happen. I was 3cm dilated and had mild contractions. They did put Pitocin to make my contractions closer. While in seating position and having my epidural in. My baby wanted to come out. I was from 3cm shoot to 10cm within seconds at that seating position. No chance to lay down side ways or having the epidural fully run through the entire body. So yes, I would say go for it and wait further.
itsallabout_mytwokids