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This report documents the program and the outcomes of Dagstuhl Seminar 25362 Optimization and Automated Reasoning for Designing Future Space Missions, which explored fundamental optimization and reasoning tasks that arise in early stages of designing complex space missions. Such tasks include selecting and scheduling the bodies that should be encountered, routing a spacecraft across multiple bodies optimally, or strategically placing facilities to support future missions. Many of these problems are still solved by hand, as current missions only contain a few celestial objects. However, with larger and increasingly complex missions, these problems become more relevant and, thus, there is an increasing need to solve space-related optimization, scheduling, and planning problems automatically. Despite the promising opportunities for collaboration, the entry barrier to many of these problems remains high for those without a background in celestial mechanics. Conversely, modern tools and techniques from constraint reasoning and optimization are still largely unfamiliar to many aerospace researchers. The Dagstuhl Seminar 25362 successfully established a bridge between computer scientists working in automated reasoning and experts from the space domain focused on mission analysis and operations. This Dagstuhl Seminar brought together researchers from academia, industry, and space agencies, fostering interdisciplinary dialogue. Problems and tools from both communities were presented in a language accessible to the other, laying the groundwork for future joint research and development.