The others have answered the same as I would have. There is no need imo to have a booster fan. I have a 4x4 with a 6" Infinity and the sides suck in as well. This helps with smell IF you decide to use a carbon filter. The round opening at the bottom(mine is 8" diameter opening) I place a long piece of flex duct, maybe 5' in length with some type of filter at the opening. This allows the fresh air to come in at the bottom while filtering the air and keeping the light out. Many use the passive intakes(the rectangular flaps) but to me it let's a lot of light in. By using the flexible duct you can run it long enough to keep the light out if your area around the tent is bright.
If you can, mount the fan outside the tent and suck the air out from the top. By keeping the fan outside it will help reduce the temps inside the tent and give you more working room.