I don't know if it can be done as automatically as you want, but you can make a reverse-telnet connection to an available modem, and use AT commands in the router to dial out:
line x y
ip host modem 3001 (address of router)
The line numbers will be those of the modems in your router. Since you have a 3620, if the modem NM is in slot 0 x will be 1. If the modem NM is in slot 1 x will be 33. y will depend on how many modems are in your NM. If you have 12 modems y will be 12 or 44.
To dial a location you can telnet to the router on port 3001. You will be connected to an available modem. From there use AT commands.
There was an application developed by Cisco, Cisco Dial Out Utility, which they decided not to support anymore. Instead they are suggesting third party applications, such as the one developed by TacticalSoftware, which does the same thing.
A free trial of the software is available at the following location:
No other thoughts. I don't think you can do that with a cisco router. You can have your users telnet directly to a modem on the router using a dialer rotary-group, but your users still have to know the dial string.
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