FARMINGTON — During Mt. Blue High School’s 43rd commencement ceremony Saturday morning, two longtime friends who were named valedictorian and salutatorian of their class shared the lectern and spoke about cooperation and how people look at problems in different ways.

Valedictorian Rosa Cohen and salutatorian Gwen Beacham said they never felt the need to compete against each other but instead discovered each had particular strengths and weaknesses that helped create a stronger solution.

“How have the two of us managed not only to stay good friends but also to help each other out?” they asked.

Throughout high school, as they worked together on many projects and assignments, they noticed a trend in their thinking, they said.

Beacham said she looks at sequences, numbers, logic, patterns and data. Cohen said she tends to look at the big picture and at the words and ideas and how it all fits together. Working alone, they would sometimes get stuck in trying to figure something out. Working together, they came to solutions.

Their message was that everyone can look at a problem in a different way and it is only when the different perceptions are put together that the best pathway appears.

“Right now, our government is paralyzed by partisanship,” Cohen said. “Many government leaders have gotten sucked into just trying to push their own agendas with little regard for what is actually going to be good for our country.”

“But think about what could get done if they just tried to work together,” Beacham said.

In a few years, some of their peers will go into government. They will all be able to vote, they said.

“We could be the generation that stops the petty bickering and actually works toward solving our country’s problems,” Beacham said.

They looked at the popular uprisings in the Middle East this spring that overthrew brutal dictators in Tunisia and Egypt, where they had ruled for decades.

“How did the rebels manage to do this? They worked together, using the power of the crowd to fight peacefully for democracy and freedom,” Cohen said.

“So get out there and work together. Let the Class of 2011 be the one to stop this competitiveness and build a new, more cooperative world,” they said.

Principal Monique Poulin said graduation day was her favorite day of the year.

“It is 13 years all summed up into one short day,” she said.

She thanked the 174 seniors for their strong support, their kindness and the respect they have demonstrated during their time at Mt. Blue.

“A little piece of you is in me,” she told them.

Poulin also said she found this student class demonstrated an amazing acceptance of others and modeled leadership qualities that she called unique.

“Thank you for being so respectful of Mt. Blue,” she said.

Senior Hannah Allen read a poem she wrote urging the class “to become people we never thought we could.” And she said, “I’ve learned from here that there’s always more to be discovered /not just in the world /but in/ myself.”

Student speaker Miles Brooks described how the high school’s adventure club, YETI, an acronym for Youth Expeditions to Ignite, “helps students use nature to search within themselves and find a greater understanding of their journey through life.”

The program included musical performances by Andreas Wyder and Claire Fletcher; Ellie Buckland, Abby Flanagan, Lena Kendall, Elizabeth Le Clair and Seth Wegner.