Thanks all for the help. I was successful at setting it up.
Now when the phone rings, the cable box pauses, the TV mutes (if she is on
Netflix), and the thermostat turns down so the loud furnace shuts off.
She then can look at the phone sitting next to her and say “yes”, “no”, or
"message" to the Voice Answer Free app and answer on speaker or reject the
call.
I also got it to un-mute the TV, un-pause the cable box, and turn the heat
back up when the call ends.
I used Tasker with the Harmony plug in and the Harmony hub.
I was going to say you can do this with IFTTT but it might not trigger right away since IFTTT is a cloud solution. If it does trigger fast enough, then IFTTT might be the easiest solution.
Unfortunately The IFTTT harmony channel/service doesn’t have mute as an option. That means you have to build an activity to do the mute, and as someone who used to do that, I can tell you it’s not easy. You may have to have a separate mute activity for different devices depending on exactly how your sound is controlled in your home theater set up.
Then Once you do the mute, you are now in the mute activity, which means you lose all of the buttons of the previous activity. So you have to switch back to the previous activity when you want to unmute.
It’s not impossible, but it’s clunky and tricky to get set up just right. And that’s without considering any issues of additional lag.