I am adding some cabinets with a sink in my laundry room, and I would like some suggestions on the best way to tie in the drain lines for the sink.

The sink will go to the left of the washing machine.  The existing washing machine drain drops vertically two feet from the valve box, there is a trap at the bottom, then it extends about two feet horizontally to the right into a sanitary tee in the main vertical drain+vent line. 

Can I tie the sink drain directly into the washing machine drain (either on the first drop or the horizontal part after the trap), or do I have to keep the sink drain separate all the way over (about 4 or 5 feet horizontal) into the main drain line?  If I have to do the latter, should it tie in above or below the washing machine line?  Does the sink drain need a separate tie-in to the vent line above?

Thanks for your help!