While his tenure at Apple (NASDAQ:AAPL) has been successful, Tim Cook has always kept a lower profile than his predecessor Steve Jobs.

In some ways that was inevitable because Jobs, especially in the last few years of his life, became a larger-than-life personality. It's very hard to follow a legend and most people stumble when faced with filling big shoes. Cook has not and while his time at the helm has perhaps lacked some of the startling innovation that marked the Jobs years, it has produced commendable results.

Cook has succeeded not by trying to be his mentor and friend, but by being himself and heeding the lessons learned from Jobs. The CEO shared some of his own wisdom, and some of what he learned from Apple's founder and longtime leader in a commencement address to students at George Washington University.

Source: GW Commencement 2015 Tim Cook from GW Media Relations on Vimeo 

Embrace the right heroes
Cook kicked off his speech by talking about an essay contest he won at 16 years old that earned him the chance to meet the governor of his state. At the time, he lived in Alabama, and the governor was George Wallace, a man who attempted to block integration of schools -- a veritable symbol of racial intolerance.

"Meeting my governor was not an honor for me," he told the graduates. "My heroes in life were Dr. Martin Luther King and Robert F. Kennedy, who had fought against the very things that Wallace stood for."

Cook pointed out that he grew up in a place where "King and Kennedy were not exactly held in high esteem." He told the tale not to share his own credentials, but to show how it's important for every person to figure out "what's right and true."

You have to make your own choices
Graduation is a time of change and Cook told the audience that they would have to go on a journey to find themselves. 

"For you graduates, the process of discovering yourself, of inventing yourself, of reinventing yourself, is about to begin in earnest," he said. "It's about finding your values and committing to live by them. You have to find your north star."

He said that everyone would face choices both easy and hard and how we make those choices defines who we are and what type of person we plan to be. The CEO said that Jobs, upon his return to Apple, had been the person who forced him to reconsider all of his own choices and reinvent his life.

Strive for greatness
When Cook joined Apple under Jobs, the company was in ruins. I had been failing for years and bringing back its founder was seen by many as a last ditch attempt to save it. Many doubted whether a turnaround was possible, but Jobs did not, Cook told the graduates. Instead, he articulated a clear plan to return the company to greatness.

"His vision for Apple was a company that turned powerful technology into tools that were easy to use -- tools that would help people realize their dreams and help people change the world for the better," Cook said.

The company's current leader bought into Jobs' vision and signed on to be part of the journey, changing everything he believed about work.

"I always figured that work was work. Values had their place. There were always things that I wanted to change about the world, but I figured that I had to do that on my own time, not in the office," he said. "Steve didn't see it that way. He was an idealist. And in that way he reminded me of how I was as a teenager."

Jobs has awakened something in his eventual successor and set him on a path to greatness. Cook urged the graduates to strive to not only change the world but do it in a way that's true to themselves.

"At Apple we believe the work should be more than just about improving your own self. It's about improving the lives of others as well," he said.