To strengthen your ideas and opinions with examples, facts, or details is to add details.

Supporting

Explanation:

As the name indicates, a "supporting" detail is there to give more support to your argument. A supporting detail is one that strengthens your position by providing examples, facts or details that bring evidence to your statements. Therefore, supporting details are essential elements in any text, as they allow you to develop your ideas, and create a more persuasive text.

i would need the dialogue to answer this.