Can I use kojic acid soap with a lactic acid exfoliator in the same routine?

Hi! I’m currently using a kojic acid soap and I also have a lactic acid water exfoliator.

I was wondering if it’s okay to use them together in the same routine like lathering the soap and then applying the lactic acid right after (or even mixing it slightly when cleansing).

Is that too harsh for the skin or could it cause irritation/over-exfoliation?

For context, my skin is type is combination and I’m mainly trying to brighten and make my skin match my neck and chest so basically even tone

If it’s not a good idea, how should I space them out instead? i also cant afford anything else, well i can. i just feel bad when i ask my parents so these are my only two options