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Craig Ruttle, Pool, Associated Press
New York Gov. Andrew Cuomo smiles after he was sworn in during an inaugural ceremony at One World Trade Center in New York, Thursday, Jan. 1, 2015. From left are his daughters Cara Cuomo and Mariah Cuomo, and right is Sandra Lee, girlfriend of Gov. Cuomo.

NEW YORK — Andrew Cuomo kicked off his second term as governor Thursday with a pep talk, urging New Yorkers to lead by example through some of the nation's worst problems.

Speaking from the symbolic heights of the newly completed One World Trade Center, Cuomo aimed high with his rhetoric, touching on national issues sure to trigger questions about his political ambitions while also hinting that he may firmly insert himself into the imbroglio that has roiled the nation's largest city.

"We work harder and we earn less. Income inequality is at the highest point in over a century. While American capitalism never guaranteed success, it did guarantee opportunity," Cuomo said. "For too many, the dream of economic of mobility has been replaced with a nightmare of economic stagnation."

Cuomo said these frequently troubled times are "a uniquely New York moment because when things are at their worst, New York is at its best."

The governor also reacted to the protests against police brutality that have swept the nation since grand juries failed to indict police officers in the deaths of black men, including Eric Garner, whose last moments were captured on videotape as he was placed in a fatal chokehold by a white New York Police Department officer.

"The world saw an African-American man in Staten Island die and people are confused, disgruntled and angry," Cuomo said. He argued that "today, sadly, too many people are questioning if the blindfold is still intact or does the justice system now see black and white or black and blue or rich and poor."

The resulting protests have driven a wedge between Mayor Bill de Blasio and New York City police unions, which have claimed that the mayor has helped create an anti-NYPD atmosphere that led to the fatal shooting of two police officers on Dec. 20.

"Law enforcement officials have been wrongfully targeted and even assassinated. It must stop," Cuomo said, before calling the two sides to work harder to find common ground. "Everyone is talking but no one is listening."

De Blasio, whose relationship with Cuomo has at times been rocky, and the head of the largest police union were both in attendance at the inauguration but did not speak.

The Democratic governor — who has been mentioned as a possible 2016 presidential candidate — took the oath of office in a private ceremony at the governor's mansion on Wednesday afternoon, alongside incoming Lt. Gov. Kathy Hochul.

The 57-year-old Cuomo, who defeated Republican Rob Astorino 54 percent to 40 percent to secure his second term, planned to travel to Buffalo — Hochul's home — to make a speech in the late afternoon.

During his half-hour speech in Manhattan, Cuomo said he wanted to focus his second term on continued efforts to revitalize upstate New York, overhaul public education and make government fairer and more effective.

He said the state had made great strides since he took office, turning a $10 billion deficit into a $5 billion surplus, expanding health care to cover 1.5 million more people, approving a same-sex marriage law, enacting tougher gun control laws and reversing gridlock and dysfunction in state government by getting Republicans and Democrats to work together.

He said the state needed to replicate reforms occurring in Buffalo throughout the upstate region and address chronic high poverty with higher wages so "you don't have to choose between paying the rent and putting food on the table."

Cuomo also paid tribute to his father, former three-term Gov. Mario Cuomo, whose health forced him to stay home.

Cuomo said he went through his speech with his father, who quipped that it was "good, especially for a second-termer."

On Wednesday, Cuomo is scheduled to deliver his state of the state address to lawmakers, who will begin their 2015 session next week.