Why do slats deploy first?
The slats help to protect the outer wing from stalling when the flaps deploy. The outer wing carries the ailerons, so there are no flaps, but the flaps inboard will induce more lift on the whole wing, raising the effective angle of attack even in the aileron section. Slats push the stall angle of attack up. Without the protection provided by the slats, the outer wing could stall, and if this happens on one wing first (very likely, there are many reasons for flow asymmetry), the aircraft will roll violently. To do so during an approach is not good at all.

Look at aircraft with powerful flaps: They all have slats at least on the outboard wing to avoid outer wing stall. One goes with the other.