Which branch can rule the presidents actions unconstitutional?

If the president is acting according to law but someone believes the law in unconstitutional and sues and the Supreme Court takes the case, it would determine the constitutionality of the law. If the president is acting illegally and violating the constitution, it would be the responsibility of the House of Representatives to initiate impeachment proceedings against the president. The Senate would then determine whether the charges were valid grounds for dismissing the president from office.