Updated at 1:50 p.m. ET

A week after a gunman killed 17 people at a Florida high school, students who survived the attack brought their #NeverAgain protest movement to Tallahassee to demand action on guns and mental health. Thousands of activists marched on the state Capitol to pressure lawmakers Wednesday, even as their peers elsewhere in the U.S. staged protests of their own in solidarity.

"Dear Congress: How can you claim to stand for the people but let your kids get slaughtered like animals in their own schools?" Sheryl Acquarola, a survivor of the shooting at Marjory Stoneman Douglas High School in Parkland, Fla., screamed to the gathered crowd on Wednesday.

"Dear Congress," she added, "how many of the thoughts and prayers that I have received do I need to check in for some damn action? Because thoughts and prayers don't mean anything without something behind it. And to be quite frank, thoughts and prayers won't stop my brothers and sisters from dying. Action will."

Between speeches, rally-goers broke out chants of "Parkland Strong" and "Vote Them Out."

Last week's shooting has galvanized students at the high school, who have begun to turn their grief into a campaign to get one of their key demands — an outright ban on assault-style weapons such as the AR-15 that was used by the alleged gunman, who was reportedly a client at mental health facilities and had been expelled from school for disciplinary reasons.

It could be an uphill battle, however. As NPR's Merrit Kennedy reports, Tuesday's session at the Capitol opened with a a prayer for the community affected by the shooting — then went on to decline opening debate on a bill banning assault weapons, while several survivors of the shooting watched the proceedings in person. Acquarola was among the students watching the vote.

"I am extremely, extremely angry and sad," 16-year-old survivor Alfonso Calderon said at Wednesday's rally, "and I don't know if I am going to be traumatized because of this. I don't know if I'm going to have faith in my state and local government anymore."

The 16-year-old junior is among about a hundred students from Marjory Stoneman Douglas High School, accompanied by more than a dozen adult chaperones, who began arriving in Tallahassee late Monday. Some of them have already sat in on legislative sessions and met individually with some lawmakers.

Many of the students emerged frustrated from those encounters, feeling their tragedy should be heard as a call to action.

"We are here to discuss with our state legislators how we can prevent what happened to us — but, as Alfonso said, I'm feeling a little discouraged about that. I don't want this to happen again. I wouldn't wish what happened to us on my worst enemy," said Sofie Whitney, 17, at the rally.

"We will not let those beautiful souls die for nothing, because we are going to make a change," she added. "We will not give up. This is only the beginning of our history. Please be on the right side of it."

Elsewhere, in Washington, D.C., hundreds of students walked out of class to express their support of the march in Tallahassee. The students in the District intended to end their own march with a rally at the U.S. Capitol. Other students across South Florida walked out of class, as well, according to CNN.

In a statement earlier this week, Florida Gov. Rick Scott, a Republican, said "swift action is needed" and that he was "bringing local and state leaders together to find solutions on how to prevent violence in our schools and keep guns out of the hands of mentally ill individuals."

Democratic State Sen. Kevin Rader, who represents Parkland, tells NPR's Morning Edition that he is optimistic the legislature can address the issue in a meaningful way: "I am fairly certain that we are going to have some changes in Tallahassee. No doubt about that."

He takes Scott at his word that Republicans — who control the state Legislature as well as the governor's mansion — can compromise on an issue they have long shown a reluctance to take up.

Rader says that unlike previous mass shootings in Florida, including the 2016 Pulse nightclub shooting in Orlando and the shooting at the Fort Lauderdale Airport in Jan. 2017, "The big difference between these three shootings is that this one happened during session, the other two didn't. So, everyone is coming back here to Tallahassee this week and for three more weeks of our nine week session ... and you can't ignore what happened."

At the federal level, President Trump on Tuesday said he had signed an executive order directing the Justice Department to move to ban bump stocks, an add-on device used to increase the rate of fire on rifles such as the AR-15. Bump stocks were used by the gunman who killed 58 people in Las Vegas last year.

"We must do more to protect our children," said Trump, who has been a strong supporter of gun rights.

As we reported earlier, "Shortly before the president made the announcement, White House press secretary Sarah Huckabee Sanders said that Trump did support 'not having the use of bump stocks,' but she declined to elaborate on any other gun measures that Trump might back other than efforts to improve background checks."

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