Jeff Bezos once told former Twitter CEO Dick Costolo that a good leader trusts his gut. Now, Costolo says Twitter's newest CEO should take that same advice to heart.

Shortly after Costolo became Twitter's CEO in 2010, his team sat down to strategize with the Amazon founder and billionaire investor, who took a stake in the company two years earlier. In the meeting Bezos told him not to run Twitter the way "the last person or the person before that ran it."