Since he was officially named Apple's CEO in 2011, Tim Cook has often told the story of the advice Steve Jobs gave him just before he died. In the memorial service at Apple headquarters, and in numerous interviews since, Cook has shared the words of wisdom Jobs bestowed on his successor.

"Among his last advice he had for me, and for all of you, was to never ask what he would do," Cook recalled in an October 19 speech at Apple headquarters. "'Just do what's right', he said."

READ MORE:Tim Cook - Stepping out of Steve Jobs' shadow

Five years later, Cook expanded on that, saying that the next best advice he received was "to be myself, to just be myself," he said in an exclusive interview with The Washington Post. "[Jobs] took away the self doubt that would naturally be there in whoever followed him. He was so smart to think about it and know what a gift it would be. There's no bigger gift he could have given me than that statement. It took away the heavy weight."

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The comparisons to Jobs of how Cook leads the company, of whether he can keep Apple's innovation engine humming, of the kind of leader Apple needs at its current size and environment, are endless. Some are favorable, others are decidedly not.

Jobs was a founder, and carried with him the great authority that comes with that role. And he was, of course, a visionary who's been called a modern-day Thomas Edison and a contemporary Leonardo da Vinci.

Cook is right when he says "it would have been a treacherous thing" to try and replace him.

Meanwhile, he's still conscious of building on what Jobs built. "That doesn't mean that I don't work like mad for his legacy."

For Cook, the comparisons to Jobs are not likely to end, especially as customers and investors wait on new mega hits that show Apple can replicate the iPhone's success. Indeed, those comparisons will probably never go away -- whoever one day succeeds Cook will probably be held up to Jobs, too.

For now, Cook seems thankful that Jobs gave his blessing to do things his own way, grounded in Apple's values.

"You can imagine the human tendency to sit and ask that question [about what Steve would have done] on so many things -- whether they're product things or this FBI thing or shareholder things or acquisitions," he told The Post. "I think that's a lot larger than people think of it. I think it's huge."