I had to be induced at 41 weeks because my waterbag had not burst though I was 3cm dilated. Doctor assisted to force waterbag break. Hours later than contractions kick in but end day I couldnt bare the pain I took jab,gas and last was epidural. That is when I get to have beauty sleep and my cervix dilate faster. I give birth next morning after more than 12 hrs in labour. But was assisted delivery as baby's heartbeat drop and head was big.
You can consult gynae/resident doctor to see if you can push it later. But as advise before when I first pregnant, it is best not to exceed past the 40 weeks. So you can try to do what you have been doing, like walking, up down stairs, squats, sex. If this does not, then you have to be induce.
All the best mummy 🤗