Which situation exemplifies the use of a president's informal powers?

The situation involving President Bill Clinton advocating for public policy reform exemplifies the use of a president's informal powers because it highlights the ability of the president to influence the legislative agenda and shape public policy through persuasion, communication, and leadership, rather than through formal constitutional or legal authority. Informal powers are those that are not explicitly granted by the Constitution but instead arise from the president's role as a leader and their ability to engage with the public and Congress.

This includes using speeches, public appearances, and personal relationships to rally support for specific policies or initiatives. Clinton's advocacy for public policy reform is indicative of how presidents work to mobilize public opinion and leverage their visibility and popularity to influence lawmakers and advance their policy goals.

In contrast, the other options illustrate actions that rely on formal powers. Appointing a Supreme Court justice is a constitutional duty, while negotiating a treaty requires the formal consent of the Senate. Similarly, delivering a State of the Union address, while significant, is a formal event meant to report on the state of the nation and to propose legislative goals, but it does not inherently involve the same level of informal influence that advocacy for policy reform entails.