Britain's decision to leave the European Union was a seismic event, a shock so profound that its backers feel they have no choice but to embark on a mission to reinvent the bloc.

Official after official has laid out his or her vision of what the EU's post-Brexit path should be, with discussions expected to culminate Friday at an informal EU summit in Bratislava.

On Wednesday, it was the turn of European Commission President Jean-Claude Juncker, one of the EU's longest-serving politicians and a fervent Europhile. He used his annual state of the union speech to lay out the course that he thinks the bloc should chart.

"What will [our children] inherit from us? A union that unravels in disunity? A union that has forgotten its past and has no vision for the future?" he asked during a speech at the European Parliament. "Our children deserve better."

"They deserve a Europe that preserves their way of life. They deserve a Europe that empowers and defends them. They deserve a Europe that protects," he added. "History will not remember us, but it will remember our mistakes. Let's not make mistakes that would put an end to the European dream."

Juncker's answer to the Brexit upheaval is, unsurprisingly, more Europe.

"I told you [one year ago] that there is not enough Europe in this union. And that there is not enough union in this union ... This assessment remains true despite the progress made," he said. "The EU is currently not in top form."

On Wednesday, Juncker laid out a laundry list of new measures that he believes the bloc should pursue, including steps to help it integrate further.

Most controversial is likely to be his call for more military cooperation, including through common military assets and a single headquarters for EU civilian and military missions.

Britain had long been averse to military integration. EU heavyweights Germany and France have now come out in favour of the cause, but some are still sceptical.

"I don't think that citizens will feel safer if the EU acts like a yobbish bloke," far-left EU parliamentarian Gabi Zimmer said. "I think many citizens instead have the creeping feeling that they will be pulled much faster into military conflicts."

Eurosceptics, meanwhile, take issue with the very idea that the lesson to draw out of the Brexit vote should be more measures to reinforce the EU.

"The more Europe you build, the more detached our citizens feel," Britain's Syed Kamall, who leads the faction of the European Conservatives and Reformists in the European Parliament, told Juncker during Wednesday's debate.

One thing many European politicians agree on, however, is that the EU has to be more convincing in tackling the issues that are of most concern to its citizens.

"Europe has to be better explained," Juncker said.

Germany's Manfred Weber also called on EU governments to stop their infighting, which he said sometimes resembles more "kindergarten than serious politics."

"[They] have to finally achieve common answers to the challenges of our times. Then people would be convinced," he said.

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