Questions / this may sound stupid

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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 😩