Should I terminate the sim?

I have lost my phone and I have anti theft installed, but I guess the phone is turned off, so I am unable to send commands to lock it. Should I terminate the sim to prevent it from being used for whatever purposes? But since avast would detect if the sim was removed from the phone, terminating it, would i cause the feature to fail, in other words, avast wouldnt be able to detect if the sim was pulled out since it isnt a functioning sim right? What should I do now?