Upgrading old plaster pool to PebbleTec how to completely kill Black Algae - new user

Hello All,

We have an old plaster pool that is in need of refinishing. Bottom is chipped in many places. Unfortunately, due to neglect, the pool has developed areas of black algae. Confirmed by puck test and business card test.

I was wondering what was the best way to completely eliminate the black algae before applying the new finish to ensure that it does not return.

My plan was to drain the pool and chlorine wash, rinse and then muriactic acid wash. Will this be sufficient, is there anything else I should know?

thanks!