Ac fan is working and also the heat, but when I turn on cool in some reason it is not working! I check out side unit a contactor not kick and I checked the inside unit I saw the thermostat wire came from out side unit not hook up with nothing those two wires sit inside the furnace. I am trying to figured out where those two wire hook up and the same time what make a contactor help him to kick? Thanks

The two low voltage wires from the outdoor unit connect to terminals Y & C on the furnace. A wire also needs to go from Y on the furnace to Y on the thermostat.