God's a big boy, he can do pretty much whatever he pleases.
There are many aspects of God, and some of them are more associated with 'active doing' than others. For example, two common archetypes are 'Father God' and 'Mother Nature'. Here the father aspect is likened to the sun, radiating light outwards and giving the spark of life to the world, while the mother aspect is like earth, accepting and nurturing. Fire and water, light and darkness, etc. are other such archetypes, one of which is 'doing' and the other 'not-doing'.
What can God do? Everything. Everything that is being done or can be done is God's doing. With God's infinite power and infinite potential, there's nothing that cannot be done.
Tricksters among you might ask a question along the lines of: "Can God make a mountain so big that even he cannot move?" The paradox of such things exist only when expressed in the limitations of language. In reality, so to say, God is creating mountains he cannot move all the time - and still remains all-powerful.
God has many aspects, and God is not limited by form. While a strong flowing river aspect of God might erode a mountain, a human form of God might have difficulties with it. And what else is a mountain if not God itself?
The power of God is unlimited in the world because the whole world is God. The potential is unlimited and even we, lowly humans, are able to tap into such greatness.