Believing that things do have the chance of getting better is probably an initial step to wanting to do anything to improve things in the first place. If you do not believe that there is any hope that things will get better, it can have a demotivating effect. Why even bother? why even try? why even do anything? why even live... it can be a miserable outcome.
If, however, we want things to get better, then I agree with you, we need to do more than just believe. We actually need to DO things to make things better. This is why we can pray, hope and believe all we want, if we don't do anything to make things happen, nothing will happen.