Cheney is the daughter of former Vice President Dick Cheney and a best-selling author and Fox News political analyst.
Stewart, 14, was attending the event with her family while on vacation in the remote Wind River mountains of central Wyoming. She presented Cheney with a signed copy of her recently published children's book, "Patrice's very own Dragon Tales."
Cheney chatted with the teen about the challenges of writing a book, her own daughter's desire to publish a book and asked about the tools Stewart used to complete the project.
Later, Stewart listened as Cheney updated the crowd on her father's medical condition after a recent heart transplant and about their experience writing a book together.
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