Make a law with additional requirements to run for Presidency.
1) You must have 5, maybe 10, years of community/public service. This sets a baseline of confidence that one is doing this for the public, that they are really in this for the right reasons. This is proof of their dedication to public service. They shall not just be a business man etc.
2) Full psychiatric evaluations must begin. There are probably more needed but that’s a start.