How can God be both omnipotent and all good?

An omnipotent being should be able to do any logically possible action. An all good being can't do an evil action. That means, for God to remain all good, there are some actions he cannot do, rendering him not omnipotent.

The response I was thinking of was that, well, he can do evil things, he simply chooses not to though, so he still has all the power to do these evil things, but chooses to remain all good. However, this isn't true, because, one of the traits of god is being all good, meaning, if God were to do something evil, he would no longer be God.