12V Trigger to trip 120V relay

I have a need to take a 12V trigger to switch a relay for a 120V device. I believe the Shelly 1 can do this, but I wanted to confirm. Also if it can handle this config, do I still have the choice of powering the device with 120 or 12v or would it have to be on the 12V side?

Appreciate it.

Appreciate the response. Given the 12V trigger is very low output, powering the Shelly 1 off it might be problematic. You mentioned ideally power/trigger from the same source, is there a negative to using a different 12V source to power it?