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Explore a groundbreaking lecture on the advancements in Large Language Models (LLMs) and their evolving capacity for complex reasoning. Delve into OpenAI's innovative o1 model, trained through reinforcement learning to generate hidden chains of thought before responding. Discover how this approach consistently improves performance with increased computational resources, surpassing previous state-of-the-art models in mathematics, programming, and advanced scientific reasoning. Examine the potential implications of further scaling this paradigm and its impact on the future of artificial intelligence and machine learning.