CRJ-700 Captain reported a Flight Attendant notified of smoke and odor in the cabin. The Flight Crew returned to the gate for maintenance.

Narrative

We were operating flight ZZZ to ZZZ1. It was a VFR night and I was conducting overnight instruction on a pilot that was getting requalified on the plane. Everything was normal up until the taxi out. After we pushed back and began taxiing; a burning smell made its way up to the cockpit. It smelled of what I thought was exhaust. My student in the left seat asked if I smelled it and I said yeah. At that same time; our Flight Attendant called up saying there's a smell as well as smoke in the cabin. She described it as a 'fog'-like smoke along with the smell. The passengers could smell it too. So at that point; we informed ATC and made our way back to the gate.As we pulled into the gate; a Left Pack Auto Fail caution message came up. I looked at the ECS (Environmental Control System) synoptic page and the output temperature was 99 degrees. I ran the QRH; which says to put the temperature control to manual. In manual mode the temperature wasn't budging from 99 degrees; which caused a Left Pack Temp caution. I ran that QRH and turned off the pack. After the QRHs were done; the smell and smoke went away. We called Maintenance and they pinged the aircraft. They said a valve seems to have gotten stuck. We deplaned and had Contract Maintenance called.[The cause was] a valve got stuck and couldn't cool the air and the pack overheated. [I suggest]; don't play with smoke.