What citizen involvement does the executive branch have?

Citizens vote on who serves the nation as president and vice-president. By voting, citizens determine which candidate receives enough electoral votes to become president. Because of this, presidents try to appear very responsive to individual citizens, often having photos taken along the campaign trail, visiting disaster areas, and hosting citizens for the State of the Union address. All of this gives the president personable traits which often translate well in the electoral process.
Citizens can also write the president. While people are more likely to write to their members of Congress, letters to the president also let citizens voice their concerns. While these letters are heavily screened by the president's staff, some letters may be turned into political action.
Citizens can also give money to a president's campaign. There is usually a method to do this when one fills out one's income taxes for the past year. Citizens can also give to political campaigns provided they keep their donations within certain limits. Citizens can also campaign for the president at the grassroots level in efforts to bring voters to the polls.
Finally, citizens can also serve the president on various committees. Many academics have served presidents as advisers in the past. Franklin Roosevelt was quite dependent on a group of academics dubbed his "Brain Trust" as he formulated the New Deal.
While the presidency is the highest office in the land, it is also one of the most visible, and it has been an American tradition to make the president appear responsive to the voters.

There are various ways that citizens are involved in the executive branch. One way is that the citizens vote for the president and for the vice president. The votes of the citizens determine which candidate receives the electoral votes that are needed to win the election.
Another way that the citizens are involved in the executive branch is that they can write letters to share their opinions on important issues with the president and the vice president. These letters could influence the thoughts of the leaders, which may, in turn, influence the policies that they will work to develop.
A third way that citizens may be involved in the executive branch is that they may serve on government boards and agencies. For example, the National Assessment of Educational Progress (NAEP) has a board that meets four times a year to discuss educational progress in the United States. Some members of this board are citizens that aren’t elected to any government office. Serving on boards such as the NAEP board is another way that the citizens are involved in the executive branch.
https://library.unt.edu/gpo/acir/Reports/brief/B-3.pdf

https://nces.ed.gov/nationsreportcard/