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See the Apple Support article(s) below.
If you can't send or receive messages on your iPhone, iPad, or iPod touch *
Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.
Try a restart.
Restart your iPhone *
Restart your iPad. *
Try a forced restart. See the section towards the end of the article.
Reset Device. -
If necessary
Hard reset. -
Do a backup and try a factory reset. Then restore from the backup.
Restore to Factory setting. *
Restore - If you see an error when you update or restore your iPhone, iPad, or iPod. *
Backup - Restore your device from an iCloud or iTunes backup. *