Sequential Recommender Systems (SRS) predict the next item of interest based on users' interaction histories and have been widely deployed, but hindered by long-tail problem. Large Language Models (LLMs), with strong semantic understanding and reasoning capabilities, offer a promising way to enrich item semantics and have recently been used as embedding generators. However, two fundamental gaps remain. First, current LLM-based embedding methods fail to exploit the model's inner reasoning capacity. Second, existing methods often inject collaborative signals implicitly via supervised fine-tuning, lacking explicit guidance for collaborative embedding alignment. In this paper, we introduce ReaEmb, a novel framework that resolves both issues via a Latent Reasoning-enhanced Contrastive Learning (LRCL) stage and a Collaborative Reward Reinforcement Learning (CRRL) stage. LRCL exploits the LLMs' inner reasoning capacity through a two-pass forward process with an additional attention module. CRRL subsequently explicitly injects collaborative signals into the LLM via a tailored reinforcement learning. Extensive experiments on three real-world datasets demonstrate superior effectiveness of ReaEmb across multiple SRS models. To ease reproducibility, we release the code online.