As Large Language Models (LLMs) advance, personalization has become a key mechanism for tailoring outputs to individual user needs. However, most existing methods rely heavily on dense interaction histories, making them ineffective in cold-start scenarios where such data is sparse or unavailable. While external signals (e.g., content of similar users) can offer a potential remedy, leveraging them effectively remains challenging: raw context is often noisy, and existing methods struggle to reason over heterogeneous data sources. To address these issues, we introduce PAT (Personalization with Aligned Trajectories), a reasoning framework for cold-start LLM personalization. PAT first retrieves information along two complementary trajectories: writing-style cues from stylistically similar users and topic-specific context from preference-aligned users. It then employs a reinforcement learning-based, iterative dual-reasoning mechanism that enables the LLM to jointly refine and integrate these signals. Experimental results across real-world personalization benchmarks show that PAT consistently improves generation quality and alignment under sparse-data conditions, establishing a strong solution to the cold-start personalization problem.