Central to it will be the EU's famous "soft power" - the economic clout and political allure that it offers to states in turmoil - and its ability to ease Russian fears that a hostile state has sprung up on its western border. Ukraine's problem is that it is in a political earthquake zone, caught in the seismic rift between the Russia of Vladimir Putin and the prosperity and democracy of the EU.
The tensions erupted last weekend after Yanukovych, an authoritarian pro-Russian leader, fled the capital Kiev when protesters refused to back a peace deal signed by their leaders. The interim leadership's first step was to demolish Yanukovych's plans of a customs union with Russia. Instead, they backed a partnership deal with the EU that the ousted President had rejected last year, triggering the crisis that led to his downfall.
Russia denounced the revolutionaries as terrorists and warned of economic reprisals. It boosted fears that Moscow might annex the Black Sea region of Crimea, home to the Russian Navy in Sevastopol, and perhaps partition the Russian-speaking eastern and southern part of Ukraine or encourage these regions to secede.
The angry rhetoric has since been dialled down, but it has had the effect of concentrating European minds on two essentials. One is that Ukraine's shattered economy depends crucially on Russia - and that a mere political declaration cannot bulldoze away a shared history. Those ties are far deeper and interwoven than those with former Soviet republics such as Estonia and Latvia, which slipped Moscow's leash to join the EU and Nato. "The EU needs to acknowledge that Ukraine is a country that will always feel close to Russia to a certain degree. Thirty per cent or more of the population have Russian as their mother tongue, there are many family links and cultural links," said Michael Leigh, former director for enlargement at the European Commission and now senior adviser to the German Marshall Fund, a transatlantic think-tank. The other essential is that, after months in which the EU flag has been waved on the streets of Kiev as a totem of freedom, Brussels now has to manage expectations.
"The Ukrainian people were for Europe because that was the only tool to modernise," Georgia's former Minister for EU relations, Thornike Gordadze, told the Herald. "They clearly were against a Russia-led customs union because being under Russian domination means a duplication of what exists in Russia - no democracy, lawlessness, corruption, that is something they wanted to avoid. That's why they were for Europe. Now Europe has to answer."
The first task for the EU is how to help keep the Ukrainian economy afloat. The interim leadership has appealed for US$35 billion ($42 billion) in emergency aid and warned of default on US$13 billion in debt if the West fails to help out. Russia had promised a US$15 billion bailout to Yanukovych, with a 30 per cent cut in the price of Russian gas, to woo him away from the EU deal, but this is now most unlikely to be unlocked.
But there is no mood of generosity in Europe these days. Budgets remain tight following the 2008 financial crisis and the eurozone's near meltdown. Germany, the biggest donor, is still smarting at the cost of bailing out Greece, which by comparison with Ukraine is a marvel of economic competence, political stability and clean business. There is even less appetite for full Ukrainian membership of the EU, which would be the next step beyond the planned partnership pact, or for membership of Nato.
EU Economic and Monetary Affairs Commissioner Olli Rehn has called for an international donors' conference - a clear indication that Brussels is playing for time, waiting for a more coherent government to emerge after scheduled May elections in Ukraine. It also shows that the EU will play a secondary role to the International Monetary Fund in any bailout, and leave it to the IMF to push through the nasty business of telling Ukraine to reform its economy in exchange for cash.
Any IMF rescue would be tied to "extremely deep reforms that would carry an extremely high social cost," said Thomas Gomart of the French Institute for International Relations (IFRI). "There will probably be a swift sense of disillusion. The situation in Ukraine remains highly combustible."
Even so, the EU also has strength in other, less visible forms: it can deliver short-term humanitarian assistance, and it can free up 610 million in technical assistance - training programmes, humanitarian assistance, educational exchange, workshops on strengthening governance and transparency and the like - that are already earmarked under the partnership deal. These programmes are not an instant fix - they are grassroots work and any results are achieved over months, if not years, rather than days or weeks.
Given the timescale, and Russia's important role as a trade partner, it could make sense to build confidence with Moscow by consulting with it on some aspects, to show that it has nothing to fear, Leigh told the Herald. "The EU ought to try to engage with Russia as much as possible at this stage. Perhaps it should get the message across clearer than it has done that these agreements are not incompatible with closer links between Ukraine and Russia."
Yanukovych's potential boltholes
Ukraine
A likely option is that former President Viktor Yanukovych is still in Ukraine.
On leaving Kiev he flew 480km east to Kharkiv where he stayed in a state residence and recorded his video message, denouncing Ukraine's new leaders. He then reportedly tried to flee the country on Sunday, out of his political stronghold Donetsk, on his private plane. However, border guards blocked him from taking off, as the jet reportedly lacked the required documents to fly. New reports suggest Yanukovych has returned to the
Donetsk region and is holed up in a three-storey bunker in the town of Volnovakha.
Crimea
Ukraine's interim Interior Minister Arsen Avakov said Yanukovych was known to have been in the pro-Russian Crimea on Monday. However, he added that Yanukovych and his
entourage had driven off to an unknown destination, having shut down their communications systems. Yanukovych had apparently holed himself up in the port town of Balaclava on Monday after attempting to fly out of Belbek Airport (12km north
of Sevastopol). Locals say he was turned away at the airport while Avakov said he changed his mind about flying when he heard that the new head of state security service was waiting for him there.
So where next?
Rumours swirled that a yacht linked to Yanukovych was spotted in the harbour of Balaclava. The 27m Bandido, and the 29m Centurion, both believed to belong to Yanukovych's son, have each been named as the possible vessel. However, the boats could be a smokescreen - some say Yanukovich left Balaclava by car.
UAE
A taxi driver in Kiev swore three days ago that Yanukovych was in the United Arab Emirates but, despite enthusiastically championing diplomatic relations between the two
nations, it is unlikely he has reached the Middle East.
Russia
Assuming Yanukovych has managed to flee abroad, the most likely options would be for him to travel to Russia or other ex-Soviet republics. Vladimir Putin has already placed the blame for the violence in Ukraine on the protesters, and strongly backed Yanukovych when in government. The duo have spoken in recent weeks but it is unclear as to whether Putin would be happy offering Yanukovych asylum.
Georgia
If Yanukovych has fled by sea from Balaclava, he would have easy access to a number of countries including Georgia. Whether they accept him, is a different matter. Yanukovych had a close friendship with Georgia's former President, Mikheil Saakashvili, but new
President Giorgi Margvelashvili condemned the violence in Kiev.
Bulgaria
Bulgaria would seem another easy choice to sail to in the Black Sea. However, the Bulgarian President Rossen Plevneliev called the ousting of Yanukovych a "democratic revolution", seemingly pledging his support for the new Government.
Belarus
Yanukovych could take heart from the precedent set in nearby Belarus. President Aleksander Lukashenko took in former Kyrgyzstan President Kurmanbek Bakiyev after he was ousted in 2010.