m0useanswered grow question a year ago Bring in new air from passive air vents at the bottom of the tent, ensure they have a dust filter on them. I have the same system as you, inline fan and carbon filter inside the tent at verry top and its sucking the air from inside the tent and pushing it out its exhaust.
Do not push the air it is sucking out of the tent back into it, it will be hot and not as fresh, want new air with fresh CO2 and less heat and humidity.
My system vents into the room it pulls from, but the room it pulls from is quite large and its vents to a area that not close to its intake vents. so it works out fine, Ideally I would vent directly outside but don't have the setup for that yet.
Good Luck!