Slice the cabbages in half lengthwise and remove the cores. Slice the cabbage into thin strips. Toss with sugar in a large bowl. If the chicken is cold, toss a few tablespoons of vinaigrette and heat in a microwave at 50% power. Add the cabbage, along with the cilantro, mandarins, almonds, and the remaining vinaigrette. Toss to combine. Season with salt and pepper.