Media playback is unsupported on your device Media caption "Mental illness pulls the trigger, not guns" - Trump's five solutions to combat mass shootings.

Two days after the US was shocked by mass shootings in El Paso, Texas, and Dayton, Ohio, the president made his first extended public statement on the attacks.

In a 10-minute White House speech, Mr Trump offered condolences, praised law enforcement and condemned the "racism, bigotry and white supremacy" he said motivated Patrick Crusias, the El Paso gunman.

"Sinister ideologies must be defeated," he said. "Hate has no place in our nation."

Those who had long pressed the president to denounce white supremacy had their pleas answered.

But critics who have called for him to address how his anti-immigration rhetoric may have given rise to that white nationalist movement will be disappointed.

Those who thought the president had offered a preview of his speech in tweets this morning will be puzzled. On Twitter, he linked support for expanded background checks on gun purchasers (something Democrats want and have passed in the House of Representatives) to his immigration reform (something Republicans want).

Instead, Mr Trump's speech made vague references to "great legislation" and called for an end to "destructive partisanship" after outlining a series of five proposals of various levels of detail and practicality.

Here they are, and what they might mean.

1) Creating tools to detect potential mass shooters online

After pledging to give the FBI "all further resources they need to investigate and disrupt hate crimes and domestic terrorism", the president turned his attention to an area where such hate and violence can often fester - the internet.

"I am directing the Department of Justice to work in partnership with local state and federal agencies as well as social media companies to develop tools that can detect mass shooters before they strike," he said.

Crusias allegedly posted a hate-filled manifesto to message board 8chan before his attack - something the mass murderers in New Zealand and Poway, California, did earlier this year.

Media playback is unsupported on your device Media caption 'Do something!' Mourners at the vigil in Dayton demand action from the Republican governor.

"An anonymous, meme-filled internet backwater, 8chan has long been a place for white supremacists to indoctrinate others - mostly young white men - into bigoted ideologies," writes April Glaser in Slate.

How, exactly, "tools" that could detect potential hate crimes will be developed and used on forums like 8chan is the key question. Decrying hate speech on the internet is easy; developing rules to regulate that online discourse in a nation that enshrines free speech in its constitution is a much more formidable task.

Last month Mr Trump held a "social media summit" in the White House, where he surrounded himself by online activists and commentators, some of whom have been accused of stirring up hatred and racial resentment - and have complained about being muzzled by technology companies.

A president who has staked out a position as opposing perceived censorship on the internet may find it difficult to promote tools that could make such censorship easier.

2) Ending the 'glorification of violence' in video games

Warning of the perils of violent video games is an old chestnut dating back to the days after the 1999 Columbine shooting, when the actions of two teenagers who murdered 12 classmates and a teacher were attributed to first-person shooting simulations and Marilyn Manson music videos.

Fifty-year-old Manson may no longer be a household name, but Republican officeholders were highlighting a video-game reference in the El Paso gunman's alleged manifesto even before Mr Trump's Monday morning address.

The president didn't outline any specific actions to control video games - and there is no conclusive evidence tying game-playing to violence - but any legislative attempts to regulate the sale of video games will run smack into a 2011 US Supreme Court case that struck down a California law criminalising the sale of violent games to children under 18.

Roughly 210 million Americans play video games. The Call of Duty franchise, which Crusias allegedly cited in his manifesto, has sold nearly 300 million copies.

If there is any nexus between violence, hate, racism and misogyny and video gaming, it's through interactions of angry young white men who talk about gaming on internet forums like 8chan, not in the games themselves.

3) Reforming mental health laws

In the 1960s and 1970s, mental health reform advocates pushed legislation that led to a significant shift away from institutionalising the mentally ill against their will and instead focused on community-centred treatment. By the year 2000, the number of Americans in mental institution had declined to 55,000 - a 90% drop from the 1960s.

In his speech on Monday, Mr Trump said that "involuntary confinement" may be necessary in some cases for those identified as mentally disturbed and prone to violence. Currently states have a patchwork of rules governing the process, although there's little scientific evidence that clinical mental illness is behind most instances of gun violence.

The president's comments echoed his brief remarks on Sunday afternoon that these mass shootings are, at their core, a mental health crisis.

Media playback is unsupported on your device Media caption The Dayton gunman had up to 250 rounds - the city's police chief says such firepower is a problem.

The key nugget in the president's discussion of mental illness on Monday was when he said that "mental illness and hatred pulls the trigger - not the gun".

It was a slightly ineloquent reprise of the popular gun-rights talking point that "guns don't kill people; people kill people".

The president may push for reform to mental health laws, but perhaps what he was really signalling was a refusal to support sweeping reform to firearm laws.

4) Enacting red flag laws

The closest the president came to a concrete gun-control proposal in his Monday speech was when he called for those "judged to pose a grave risk to public safety" not have access to firearms and, if they own them, to have a "rapid" process to allow law enforcement to take them away.

Such red flag laws have had some support from gun-control activists, although they're viewed as only a partial measure. Gun-rights groups, on the other hand, have been highly sceptical of a process that would allow law enforcement officials to unilaterally suspend what they believe should be an unfettered constitutional freedom.

Media playback is unsupported on your device Media caption One US sheriff campaigned for so-called red flags laws - the other refuses to enforce them.

Some mental health advocates are similarly wary that such legislation might deter individuals from seeking treatment and further stigmatise those with mental health issues.

Several Republican senators have already expressed interest in backing a federal red-flag law, which could indicate congressional action is possible.

Fifteen states currently have some form of the legislation. The Colorado law, passed by Democrats in April, has provoked widespread anger among the state's conservative community, however, including promises from some local officials not to enforce the rules when they go into effect next year.

It's safe to say that federal legislation will prompt similarly vigorous opposition.

5) Fast-tracking death penalty for terrorists and mass murderers

Two weeks ago, Attorney General William Barr announced that the federal government would resume executing individuals on its death row for the first time in 16 years. On Monday, the president called for the expansion of capital punishment for those convicted of mass shootings and "hate crimes".

The death penalty may be losing popularity and declining as a punishment in the US, but polls indicate it is still backed by a majority of Americans for particularly heinous crimes. The president, who has criticised what he sees as the lenient treatment and drawn-out appeals processes provided to convicted criminals, may view this as a popular proposal that puts his liberal opponents out of step with the popular will.

Whether a more vigorous use of the death penalty will have any deterring effect on mass shootings - which frequently end in suicide - is an entirely different question.

As for the death penalty for "hate crimes", some conservatives view such legislation - even when it doesn't involve capital punishment - as restricting free speech and creating a special class of victims based on the perpetrators discriminatory "state of mind".

In other words, Trump's justice department may come up with new legislation, it may even be popular in the abstract, but there probably won't be many people in Congress fighting to make it law.

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