You can absolutely use the tablets to help raise the CYA levels--just keep an eye on your pH and make sure it doesn't get too low--trichlor tabs are acidic and can drive pH downward. It's fine to use the tabs and the bleach at the same time in the pool--after all, it's all chlorine when it gets in the water. Just don't let the bleach and tabs come into direct contact with each other before they're in the pool.

Janet