Student peer review writing is prevalent and important in education for fostering critical thinking and learning motivation. However, it often entails challenges such as high effort and writer's block. Leaving students unsupported may thus diminish the efficacy of the process. Large Language Models (LLMs) offer a potential remedy, but their utility hinges on user-centered design. Guided by design-determining constructs from the Cognitive Process Theory of Writing, we developed an intelligent writing support tool to alleviate these challenges, aiding 1) ideation and 2) evaluation. A randomized experiment (n=120) confirmed users were less inclined to utilize the tool's intelligent features when offered pre-supplied ideas or evaluations, validating our approach. Moreover, students engaged not less but more with their writing if support was available, indicating an enhanced experience. Our research illuminates design choices for enhancing LLM-based tools' usability and user experience, specifically optimizing intelligent writing support tools to facilitate student peer review.