How to use custom price attributes in shopping cart price rule, replacing the regular price?

Question

What I'm trying to set is a promo shopping cart rule that uses custom price attribute.

The rule should go like this:

If ALL of these conditions are TRUE :

1. Price in cart equals or greater than 200.
2. HERE I NEED TO ACTIVATE CUSTOM PRICE ATTRIBUTE

So what I'm trying is to make sure that when a customer reaches a certain amount in shopping cart sub total, the regular price will be replaced with the custom price attribute.

Is this possible and can you help me solve my issue?