The ceremony featured poetry, humor and musical performances by a range of senior class members, including Eddie Zhou, Jack Kwan, Alena Rott, Allison Hannah, Fiona Flynn and Jeff Neff.
Maggioncalda struck a somber note, describing her weeks of depression and "total exhaustion."
The four-sport athlete, straight-A student and homecoming queen told classmates she felt "overcome by total exhaustion and a sense of sadness that I couldn't control.
"I couldn't do my homework and I stumbled through basketball practices in a daze. I slept 14 hours a night and woke up exhausted and in tears."
She missed three weeks of school.
"I would cry and I wouldn't know why. I couldn't stop. I felt empty. I felt lost. I felt alone."
Maggioncalda said she got help from her family, her teachers, her doctor and a few friends.
When she finally returned to school, she "heard that people thought I wasn't at school because I was celebrating getting into Stanford early," she said.
"Let me tell you, the lives of others are not always what they seem."
Looking back, Maggioncalda concluded that her four-year obsession with getting accepted by a top college had caused her to miss out on the richness of high school.
"I've often felt alone during high school," she said. "How is it possible to feel so alone when constantly surrounded by classmates and teammates?
"It's because I felt insecure and I was obsessed with my future. I didn't feel close to my friends or appreciate each moment I was living.
"I was afraid — afraid that not getting into a top school would render my past a failure and my future doomed."
Maggioncalda drew laughs and cheers from the audience when she recalled some of the high points of her class's four years at Gunn — a hard-fought championship basketball game and this year's seniors winning the school's traditional "airbands" competition.
"Please don't get me wrong; there were definitely some great times in high school," she said.
Maggioncalda said she'll make a point of appreciating such moments "more deeply" in the future, rather than rushing on to the next thing.
She plans to take a gap year, "put my future on hold so I can enjoy the present. So I can wake up each morning looking no further than just the day ahead.
"And once I go to college I'm going to learn for enjoyment, not for the A. I'm going to make deeper connections with the people around me and spend less time on Facebook, Twitter, Instagram and whatever else gets invented in the next 12 months," she said.
Maggioncalda said she recently shared some "senior wisdom" with a group of freshmen in one of her classes.
"I told them to quit obsessing about the future and enjoy every day they have at Gunn and love the people around them," she said. "I told them I made the mistake of rushing through my four years here, thinking only about my future, and I regret that.
"We've learned a lot during our four years at Gunn ... and most of it is important and we should take it with us.
"But some of what we've learned is unhealthy and should be left behind. We should not sacrifice relationships with people for a letter on a piece of paper.
"So, people, take the good things from Gunn to your new schools next year and make the most of it. All of us will be happy at any college we go to as long as we connect with the people around us and feel like we belong.
"Live now. Share deeply," Maggioncalda said.
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