And that is exactly how we think. We think in narratives all day long, no matter if it is about buying groceries, whether we think about work or our spouse at home. We make up (short) stories in our heads for every action and conversation.
Actually, I think in images. The only dialogue in my head is my own voice. Whether I'm doing mathematics or programming, it's images combined with me speaking internally about it (trying to reason my way through it). Perhaps that's a "story", but it'd be a boring one. Maybe there's a more precise term?
When you're reasoning through a problem, what does it look and sound like to you, mentally? Does anyone else think in pictures?