Large language models (LLMs) are impressive, but they've always struggled with fact-checking themselves. Imagine an AI writing an article and then confidently asserting incorrect information – a frustrating limitation. New research suggests a clever solution: 'key condition verification.' Instead of asking the LLM to broadly critique its own work, researchers mask a crucial piece of information in the original question and then ask the LLM to solve for it, using the AI's initial answer. Think of it like a reverse logic puzzle. If the LLM's original answer is correct, it should be able to reconstruct the masked 'key condition.' This method, called 'Progressive Correction' or PROCO, iteratively refines the LLM's responses, leading to significantly improved accuracy in complex reasoning tasks like math word problems, open-domain question answering, and commonsense reasoning. Experiments show PROCO boosts performance across various LLMs, including both commercial models like GPT and open-source alternatives. This breakthrough could lead to more reliable and self-sufficient AI systems, capable of verifying their own outputs without constant human oversight. While promising, the research is still in its early stages. Challenges remain in applying this technique to non-English languages and more complex, nuanced problems. However, the potential for self-correcting AI is immense, paving the way for more trustworthy and autonomous applications in the future.