Questions / this may sound stupid

I've heard of women being induced and it not working and them being sent home after being dilated to 1cm and being monitored for 12 hours so I was wondering. When I go in to be induced (I'm already 1cm dilated and my cervix is starting to thin out) if it doesn't work what is their next step? I may sound stupid but it's my first time and I'm worried I'll have to wait longer to have my baby and I'm already 40 weeks.

Please don't judge I have no idea how this works and I'm worried 😩