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NEW: Greece remains "in a particularly critical crossroads," Papademos says

Newly sworn-in prime minister expresses optimism that Greece can fix its economy

Implementing the bailout package will be the government's "main task"

Athens, Greece CNN  — 

Greece’s new prime minister told Parliament Monday that staying in the eurozone “is the only choice” as his country seeks to avoid default.

“We can prove we are able to change the country and to shape a positive prospect for the future and especially for the young people,” Lucas Papademos said. “It is within our abilities. We have this power. … I believe we will manage to achieve these goals.”

Papademos, who took office last week after George Papandreou stepped down, said his government’s “main task” will be to implement a bailout package brokered on October 26.

He cited “a crisis of trust” among the country’s European allies about whether Greece has the will and the ability to restore its economy, but said “big progress” has already been made toward restoring fiscal stability, citing the reduction of the deficit from 15% of GDP to 10.6%.

“The competitiveness of the Greek economy has improved considerably,” he said. But, he added, Greece remains “in a particularly critical crossroads.”

He said fiscal support is needed from Greece’s European allies and the International Monetary Fund.

The October 26 bailout, worth 130 billion euros ($177 billion), calls for austerity measures but “will ensure the financing of Greece over the following years and the completion of the effort of the economic recovery.”

Papademos said work should get under way “immediately, at a very high pace,” with the first priority being to secure disbursement of the next tranche of bailout money from a 2010 bailout package by no later than December 25 to ensure the government can pay its bills.

Though the Greek people and their economy face an uphill slog, the costs and sacrifices are to be distributed fairly, he said. One thing is not negotiable: “Staying in the euro is the only choice,” he said. “This crisis can turn into an opportunity if we just all of us do our best.”

Papademos, a former banker and European Central Bank vice president, became his country’s interim prime minister Friday after several days of political wrangling.

The drama in Greece has shaken international markets because investors were afraid the new bailout deal – which has stringent austerity measures attached – might not be implemented.

Papademos previously has stressed Greece’s commitment to the euro, saying its membership in the eurozone, the 17 nations that use the euro as currency, is a guarantee of financial stability.