In this study, we aim to address the task of assertion detection when extracting medical concepts from clinical notes, a key process in clinical natural language processing (NLP). Assertion detection in clinical NLP usually involves identifying assertion types for medical concepts in the clinical text, namely certainty (whether the medical concept is positive, negated, possible, or hypothetical), temporality (whether the medical concept is for present or the past history), and experiencer (whether the medical concept is described for the patient or a family member). These assertion types are essential for healthcare professionals to quickly and clearly understand the context of medical conditions from unstructured clinical texts, directly influencing the quality and outcomes of patient care. Although widely used, traditional methods, particularly rule-based NLP systems and machine learning or deep learning models, demand intensive manual efforts to create patterns and tend to overlook less common assertion types, leading to an incomplete understanding of the context. To address this challenge, our research introduces a novel methodology that utilizes Large Language Models (LLMs) pre-trained on a vast array of medical data for assertion detection. We enhanced the current method with advanced reasoning techniques, including Tree of Thought (ToT), Chain of Thought (CoT), and Self-Consistency (SC), and refine it further with Low-Rank Adaptation (LoRA) fine-tuning. We first evaluated the model on the i2b2 2010 assertion dataset. Our method achieved a micro-averaged F-1 of 0.89, with 0.11 improvements over the previous works. To further assess the generalizability of our approach, we extended our evaluation to a local dataset that focused on sleep concept extraction. Our approach achieved an F-1 of 0.74, which is 0.31 higher than the previous method.