However, a native speaker (from Britain) told me that I should use go on. Maybe this is a case of American vs British English?
"Go to the next step" and "go on to the next step" have very similar meanings. The choice of which to use depends on context and the flow on the sentence. Sometimes a phrase feels like it should be abrupt and to-the-point. Other times, more expansive and wordy. Even the same author might vary this choice, to create a desired effect.