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The woman, who was identified as Nora Barré, stood up at a Bush town hall event in New Hampshire on Wednesday night and asked him about his plan to accept refugees from the war-torn country.
"I'm Syrian-American. I have 14 family members that just left Syria. Their house was bombed. Their livelihood ... I've been supporting them the last five years just to eat, and I just got them out to Turkey," she said, appearing to tear up as she spoke.
"I just want to know, what are we going to do to help? Are we going to let Putin run this world?" she asked, referring to Russian President Vladimir Putin, who authorized the start of Russian airstrikes in Syria on Wednesday. "He's a dictator. He cannot have the world stage. And that's what's happening. ... So I'd like to know your views."
Bush said he applauded Barré's act to care for her family. His response offered a notable contrast to Republican front-runner Donald Trump - who, miles away at an event in New Hampshire, said if he were elected president, refugees would "go back."
Bush discussed his daughter-in-law, Sandra, who is of Iraqi and Jordanian descent. He referenced the brutal slaughter of thousands of Iraqi Christians last year at the hand of the Islamic State terror group. He said the larger crises in the Middle East were a result of a US pullback in the region.
"This is normally what we do unbelievably well. We act on our heart. We organize it well. We take care of people," Bush said.
"Assad is a brutal dictator. He barrel bombs his innocents - he kills them. He's destroying communities. Two hundred thousand-plus people have died. And people are leaving, not because they're immigrants looking for a better life. They're leaving because they'll die. It's that simple. And we have to play a role in providing support," he added. "We're duty-bound to provide support."
Bush further dinged Trump during a Thursday appearance on MSNBC's "Morning Joe."
"This is not an America that I believe is the one that will create peace and security. America's values matter, and America's strength matters. And both of those things are at risk right now because of what's going on," Bush said.
When his campaign highlighted the clip on Facebook, it earned a response from Barré: "#YouRAwesome."
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