Help with connecting gear

I have a multi-track recording in Ableton Live 7.  I want to remix it using the following gear.  (I know I can mix the tracks in Live but I want to use the hardware mixer instead):

Alesis MultiMix 12R mixer.

Presonus FP10 10x10 firewire audio interface.

Is it true that I can assign the individual tracks in Live to individual outputs on the FP10, then connect the outputs of the FP10 using TRS cables to the inputs of the mixer, then mix the tracks by adjusting volume, pan and EQ?

How would I then record the final mix back to Live? 

Or would I just record the final mix as stereo to CD using the left and right outputs of the mixer.

 Thanks!!


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