Worried with no sign of baby coming out...

Hey mama! First thing: breathe! You’re doing such a great job that baby is so happy and comfy in the tummy that he doesn’t want to come out so give yourself a pat on the back! Second, research has shown that 40 weeks isn’t the absolute die die labour date and that 42 weeks might be the new overdue date :) As for induction, there are many natural methods that you can try. Here’s a link you could take a look at for the natural options you can consider as well as options for an induction: https://www.webmd.com/baby/inducing-labor-naturally-can-it-be-done