The application of machine learning models to complex problem-solving tasks has revolutionized various domains by enabling machines to perform sophisticated language and reasoning tasks with a high degree of proficiency. Introducing a novel hybrid approach that integrates trial-and-error methodologies with chain of thought (CoT) reasoning significantly enhances the problem-solving capabilities of large language models. This research implemented and evaluated this innovative approach within the open-source Llama model, demonstrating substantial improvements in solution accuracy and logical consistency across a variety of complex tasks. The hybrid model alternated between generating hypotheses, evaluating them, and refining them through an integrated feedback loop and CoT framework, allowing continuous learning and iterative enhancement of solutions. Comparative evaluations with baseline models highlighted the superiority of the hybrid approach, showcasing its potential to produce accurate and coherent solutions. The study's findings contribute to the development of more robust and reliable models capable of addressing intricate reasoning challenges with greater precision and coherence, paving the way for advanced applications in artificial intelligence.