Reflective writing is known to support the development of students' metacognitive skills, yet learners often struggle to engage in deep reflection, limiting learning gains. Although large language models (LLMs) have been shown to improve writing skills, their use as conversational agents for reflective writing has produced mixed results and has largely focused on providing feedback on reflective texts, rather than support during planning and organizing. In this paper, inspired by the Cognitive Process Theory of writing (CPT), we propose the first application of LLMs to the planning and translation steps of reflective writing. We introduce Pensée, a tool to explore the effects of explicit AI support during these stages by scaffolding structured reflection planning using a conversational agent, and supporting translation by automatically extracting key concepts. We evaluate Pensée in a controlled between-subjects experiment (N=93), manipulating AI support across writing phases. Results show significantly greater reflection depth and structural quality when learners receive support during planning and translation stages of CPT, though these effects reduce in a delayed post-test. Analyses of learner behavior and perceptions further illustrate how CPT-aligned conversational support shapes reflection processes and learner experience, contributing empirical evidence for theory-driven uses of LLMs in AI-supported reflective writing.