Unit tests play a vital role in the software development lifecycle. Recent advances in Large Language Model (LLM)-based approaches have significantly improved automated test generation, garnering attention from both academia and industry. We revisit LLM-based unit test generation from a novel perspective by decoupling prefix generation and assertion generation. To characterize their respective challenges, we define Initialization Complexity and adopt Cyclomatic Complexity to measure the difficulty of prefix and assertion generation, revealing that the former primarily affects compilation success, while the latter influences test coverage. To address these challenges, we propose Seed&Steer, a two-step approach that combines traditional unit testing techniques with the capabilities of large language models. Seed&Steer leverages conventional unit testing tools (e.g., EvoSuite) to generate method invocations with high compilation success rates, which serve as seeds to guide LLMs in constructing effective test contexts. It then introduces branching cues to help LLMs explore diverse execution paths (e.g., normal, boundary, and exception cases) and generate assertions with high coverage. We evaluate Seed&Steer on five real-world Java projects against state-of-the-art baselines. Results show that Seed&Steer improves the compilation pass rate by approximately 7%, successfully compiling 792 and 887 previously failing cases on two LLMs. It also achieves up to ~73% branch and line coverage across focal methods of varying complexity, with coverage improvements ranging from 1.09* to 1.26*. Our code, dataset, and experimental scripts will be publicly released to support future research and reproducibility.