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Changes the part numbering system to be dynamic, resetting the part counter for each new division encountered, as defined by the `division` field in the YAML configuration. This simplifies the logic and makes part numbering more flexible, allowing for different numbering schemes within different divisions of the book. It also replaces the static numbered part ordering with a more robust, type-based routing approach for LaTeX command selection. The `type` field in `book/part_summaries.yml` is used to determine the LaTeX command to use, instead of relying on hardcoded key names.