Which of these actions can a President take through an executive order?

A President can take action through an executive order primarily to manage the operations of the federal government. Executive orders are directives issued by the President to manage the executive branch and carry out laws that have been passed by Congress. This allows the President to implement and clarify existing laws, direct operations within the Department of Justice, enforce federal regulations, and shape policies within the executive branch.

Creating new tax laws is within the purview of Congress and requires legislation rather than an executive order. Impeaching officials is a power exclusively granted to Congress, specifically the House of Representatives for the impeachment process and the Senate for the trial. Similarly, appointing members of Congress is not a power held by the President, as members of Congress are elected by the people and cannot be appointed by the President. Thus, managing the federal government’s operations through executive orders is the correct action that falls within the President's authority.