It's a conundrum President Joe Biden's advisers haven't yet found a way to solve: The commanding figure they see on the world stage isn't viewed by many voters that way back home.

The president's advisers see lengthy days in far-flung time zones, a canny ability to convene fellow heads of state and an understanding of global politics honed over a half-century career. Most voters in the US see something else -- a CNN poll last week showed about three-quarters of Americans say they're seriously concerned that Biden's age might negatively affect his current level of physical and mental competence.

Reconciling those competing visions will be a singular challenge for Biden as he ramps up his reelection campaign. For the president and his advisers, foreign trips -- unfurling at a breakneck pace, with little sleep -- are often an opportunity to dispel notions that the 80-year-old president is too old to do the job and are increasingly leaning on these trips to make their case.

Traveling to New Delhi and Hanoi over the past several days, Biden sought to seize the opportunity. He darted from leader to leader for quick informal talks in the summit hall, seeking to cultivate the interpersonal connections that have been his hallmark.

He was able to seal significant agreements on global infrastructure projects, debt reform for the developing world and, most consequentially, challenged China's sphere of influence by elevating relations with Vietnam, drawing bipartisan praise in Washington.

Between his events, Biden found time to speak by phone with US Open champion Coco Gauff and receive briefings of the devastating earthquake in Morocco.

The round-the-world trip concludes on Monday with a single marathon day that has already contained four separate meetings with Vietnamese leaders, a state luncheon and a visit to a site honoring the late Sen. John McCain. The president is now on an 11-hour flight to Alaska, where he'll hold an event with service members marking 9/11 before finally making another six-hour flight to Washington.

"This around-the-world-in-five-days is interesting, isn't it?" he joked — sort of — at a Sunday news conference.

Over the course of the 26-minute press availability, Biden did display a command of the foreign policy issues at the heart of his trip as he touted the rapprochement he had secured with Vietnam.

The event also put on display the verbal stumbles, difficulty hearing and long-winded, not entirely relevant anecdotes that give Biden the appearance of the octogenarian he is, rather than the decisive commander-in-chief his aides would like the public to see.

Biden ended his news conference by telling reporters: "I am going to go to bed."

As Biden's reelection campaign begins ramping up, it has begun to use his foreign trips to make an implicit argument against concerns about Biden's vitality.

An ad released ahead of his trip last week highlighted his February visit to Ukraine, seeking to draw foreign policy contrasts with Republicans but also working to portray the president in a vigorous light.

"In the middle of a war zone, Joe Biden showed the world what America is made of. That's the quiet strength of a true leader who doesn't back down to a dictator," a narrator says in the spot, which aired during "60 Minutes" in Phoenix, Atlanta, Detroit, Las Vegas, Raleigh, Philadelphia and Milwaukee markets.

That trip, which involved a nine-hour train ride in and out of the war zone, has been a reliable talking point for Biden's aides when answering tough questions about their boss's age.

"He was there with the alarms blaring in the back. And people were so impressed that he was able to be there and look strong and represent the American people in Kyiv, in a war zone country," White House press secretary Karine Jean-Pierre said last week.

Other advisers point to an episode at last year's G20 summit in Bali, when Biden was awoken in the middle of the night with news a rocket had landed in Poland along the Ukraine border. Biden worked the phones through the evening and swiftly arranged a meeting of allies at his hotel, hoping to defuse a potentially explosive situation with a NATO ally. Jet-lagged officials said the president didn't miss a beat.

Still, examples of the president's stamina have been paired with moments Biden did not appear as energetic. He has previously skipped nighttime leaders' dinners at past summits, including at a NATO gathering in July. He did attend an evening event at the G20 this weekend, arriving at 8:32 p.m. and departing more than an hour later.

"These things are often of value in terms of building relationships with key people," Biden's deputy national security adviser, Jon Finer, told reporters Sunday aboard Air Force One.

Biden's current political weaknesses do not go unnoticed by fellow world leaders, most of them politicians themselves who are highly attuned to the electoral landscape.

The prospect of Donald Trump returning to the White House has been the subject of speculation and, for many, concern. Governments around the world keep close tabs on the American election and the legal dramas currently surrounding the former president.

Inside the G20 summit hall in New Delhi, the topic of the forthcoming American election did arise among world leaders, according to US national security adviser Jake Sullivan.

"It wouldn't be credible to say that American politics is not something that that comes up in conversation," he told reporters in New Delhi.

Still, he said the 14 months until next year's election means many leaders are only taking passing interest.

"In most countries, elections tend to last weeks, two months, not the endless marathon that is the American presidential election," he said. "It is still only September of 2023. But you know, it's part of the conversation but not a central part of the conversation around here."

Indeed, the principal focus in India was on the developing world and making the argument for a sustained US role in it.

Much of his efforts took place behind closed doors, in large part due to press coverage restrictions imposed by the Indian hosts. When he was seen by reporters, it was mostly at photo-ops, including at the Raj Ghat memorial for Mahatma Gandhi, where he removed his shoes and wore a traditional scarf to lay a wreath.

When Biden did speak publicly in New Delhi, it was to unveil a major new project connecting India to the Middle East and Europe with a new transit corridor. The project is monumental in scale, a modern-day spice route that — if realized — would directly challenge China's own efforts to expand global trade. It required extensive deliberations with multiple governments, some of whom don't get along. During his presentation of the plan, Biden hailed the project as a "real big deal" for jobs, supply chains, trade and global connectively.

Biden was more visible at his second stop in Hanoi, including during the news conference, meetings at the Communist Party headquarters and a visit to a commemoration marker near the place Sen. John McCain was shot down in the Vietnam War.

When Biden convened his news conference Sunday evening, the time zone difference was understandably jarring.

"It is evening, isn't it?" he wondered to laughter.

Amid the near-constant questions about Biden's age, it was perhaps welcome when Vietnam's General Secretary Nguyễn Phú Trọng offered the president a compliment.

"You have nary aged a day and I would say you look even better than before," he said. "Every feature of you, Mr. President, is very much complimentary of your image."

Biden laughed.