The end of the party conventions marks the point in a presidential campaign when candidates shift from trying to rally their natural supporters to trying to impress an entire nation of voters.

Hillary Clinton and Donald Trump have a lot of work to do.

As the race to the Nov. 8 election looks now, both sides should see reasons for optimism. An average of national polls showed Trump surging to take a narrow lead in the days after the Republican convention. At the same time, prognosticators still said Clinton is more likely to end up winning, in part because of Democrats’ presumed advantage in states that count more in the Electoral College.

Everybody should expect this to be a close contest that leaves half the electorate – at least – dissatisfied.

As ever, the result is going to depend in part on the candidates’ ability to motivate their natural base of support to go to the polls. The fractious conventions confirmed that those natural bases are weaker than usual because of many Bernie Sanders supporters’ continued opposition toward Clinton and many conservatives’ antipathy toward Trump. Still, some Clinton and Trump backers would never consider switching sides.

And perhaps more than ever, it’s going to depend in part on their ability to win over nonpartisan voters and even pick off disaffected voters from the other party. The polls suggest there are a lot of disaffected voters.

Both Trump and Clinton should recognize that if they continue to fail to impress, then Libertarian Party candidate Gary Johnson could gain the polling percentages necessary to qualify for the debates. There, Johnson could help to highlight concerns about how a President Donald Trump or a President Hillary Clinton might misuse federal power.

Clinton’s and Trump’s convention speeches highlighted their strengths, but also their weaknesses, and left each with much to prove.

Trump must prove that his claims that “I alone” can fix what ails America aren’t the words of a snake-oil salesman who doesn’t know his own limits – or the government’s constitutional ones. He must prove his assessment of the nation’s problems is accurate and not just fearmongering and scapegoating. He must prove he has clear, workable solutions. He must answer the concern that his hair-trigger temperament makes him an unsuitable commander in chief.

Clinton must show that her much-touted cool-headedness and experience in government don’t make her an unimaginative tool of the establishment. She must explain why Americans shouldn’t see worrisome implications in her carelessness with top-secret email. She must confront, not dismiss, the terrible things people have said about her for decades, and convince voters that not all of them are true.

Clinton and Trump share one obstacle: trust.

Clinton is widely viewed as a liar. Yet Trump’s statements on the campaign trail are generally rated far worse than Clinton’s by fact-checking journalists.

As the campaigns go national, voters must exercise their critical thinking and continue to judge the candidates by the standards expected of a would-be president.