Not acting on sadness means seeing it in such a way that precludes acting on it. The same goes for anger and every other experience.
We are not in control of our reactions, they are a direct result of our perceptions. This is why there is a focus in Buddhism on mindfulness, because it evokes a nonreactive perception of experience, allowing us to dwell independent of our experiences (anissito ca viharati - MN 10).
So, we remind ourselves for example "sad, sad..." or "angry, angry..." to evoke clarity and purity in our perception. That in turn prevents reactivity by its very nature.