How do I cool a HPS Bulbs reflector and carbon filter, all inside the same unit.

I have a grow box and I'm confused on how I am going to cool the reflector, and use the carbon scrubber. Would I have ducting on the reflector, and a fan pulling air from the reflector at the end, then place the opening close to the carbon scrubber, which is pulling air out of the box?

Here is a pic to explain

BTW, the box inside a box is the reflector, the black stuff represents the tubing, and the red is a fans, with the arrow directing their airflow


ALSO
why not get these cheapo fans
High Tech Garden Supply
Valueline 6 Inch Centrifugal Inline Fan - Businesslights.com

over these expensive ones

Vortex 6 inch 449 CFM High Power Inline Fan - Businesslights.com
High Tech Garden Supply
or even High Tech Garden Supply

Fans confuse me

U would have to duct the air in ur grow box into ur cool tube if the filters connected to the tube and venting out of the room....To maxumize efficiency ur going to need ur box air tight.

Isnt that what i'm doing in the picture?

or do you mean it should go like this

inside ==Carbon filter==(cool tube)====->fan->== OUTSIDE

NAH i was thinking it all wrong didnt see the pic originally. I thought u said that u were connecting the carbon fillter to the exhaust end of the inline cool tube naturally the only way u would be able to filter the air in the room is by ducting or blowing the air u want filtered in to the cool tube to be filtered.
I was thinking inline, but it would be better to hook up ac duct to one end -carbon filter to the other and blow the air into the tube to be exhausted.

So

[Carbon filter]==>>Fan>>==(Cool Tube)=== Outside

? Is what you are saying...

also what fan would be able to do that? Its gonna be a 3x2x3 box probably.

Lol No bro i was thinking inline cool tube for ur hps something like this:

A/C-(outside air)-> COOLTUBE/LAMP -> CARBON FILTER-> Outside Air
BUT venting the Air inside the grow box ^ into cooltube chamber to be vented to the outside thru the filter