You do not want to do that if you want to use the TFP method. Greenout (This is the stuff I assume you mean
https://islandrecreational.com/green-out-premium-pool-shock-1-lb-bags-fast-acting-formula/) adds CYA to your water.
It is certainly your pool and you're free to treat it as you see fit. But, our advice is to not use any Greenout until and unless your CYA falls under the, say, 30-40 range. If you do, your CYA will go up and you've done a lot of work to bring it down.
Our recommendation is to chlorinate with liquid chlorine only. A second choice is Calcium Hypochlorite which will add Calcium to your water. That may or may not create problems for you. That will be dependent on your calcium level which you will know when your test kit arrives and you test it.
My recommendation is to sell your Greenout to someone who does not use TFP method. The price is probably around $10/bag this season. Alternatively, keep it until some year when your CYA is too low.
We've told you what we'd do. Your choice on whether or not to do that or something else.