The recent advancements in Large Language Models (LLMs) have generated considerable interest in their utilization for sequential recommendation tasks. While collaborative signals from similar users are central to recommendation modeling, effectively transforming these signals into a format that LLMs can understand and utilize remains challenging. The critical challenges include selecting relevant demonstrations from large-scale user interactions and ensuring their alignment with LLMs' reasoning process. To address these challenges, we introduce AdaptRec, a self-adaptive fram-ework that leverages LLMs for sequential recommendations by incorporating explicit collaborative signals. AdaptRec employs a two-phase user selection mechanism -- User Similarity Retrieval and Self-Adaptive User Selection -- to efficiently identify relevant user sequences in large-scale datasets from multi-metric evaluation. We also develop a User-Based Similarity Retrieval Prompt, enabling the model to actively select similar users and continuously refine its selection criteria during training. Using the collaborative signals from similar users, we construct a User-Contextualized Recommendation Prompt that translates their behavior sequences into natural language, explicitly integrating this information into the recommendation process. Experiments demonstrate AdaptRec's superior performance, with significant improvements in HitRatio@1 scores of 7.13\%, 18.16\%, and 10.41\% across real-world datasets with full fine-tuning, and even higher gains of 23.00\%, 15.97\%, and 17.98\% in few-shot scenarios.