2024 SSMO Speed Round Problems/Problem 4

Problem

Sam wants to read the \textit{Harry Potter} and \textit{Warriors} books. There are 7 \textit{Harry Potter }books that must be read in a specific order, and there are 6 \textit{Warriors} books that also must be read in a specific order; however, he can read the two series at the same time. For example, he could read the first three \textit{Harry Potter} books, then the first five \textit{Warriors} books, then the remaining \textit{Harry Potter} books, and finally the last \textit{Warriors} book. In how many unique orders can Sam read the books?