Like most federal employment, the Presidency should have a one-year probationary period. At the conclusion of one-year, we get to vote on their performance. Popular vote only, if below 50%, a snap election has to be held within 90-days under standard general election rules and they can run again.
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If presidential immunity can be law, so can a presidential probationary period.
It doesn't say that's the end all.
The Westminster system has our Prime Minister elected from within the winning party. If they turn out to be mad, the party replaces them with another MP.
50% of all voters seems like a reasonable expectation for a leader of all voters (whether they vote or not).