Urban planning faces a critical challenge in balancing city-wide infrastructure needs with localized demographic preferences, particularly in rapidly developing regions. Although existing approaches typically focus on top-down optimization or bottom-up community planning, only some frameworks successfully integrate both perspectives. Our methodology employs a two-tier approach: First, a deterministic solver optimizes basic infrastructure requirements in the city region. Second, four specialized planning agents, each representing distinct sub-regions, propose demographic-specific modifications to a master planner. The master planner then evaluates and integrates these suggestions to ensure cohesive urban development. We validate our framework using a newly created dataset comprising detailed region and sub-region maps from three developing cities in India, focusing on areas undergoing rapid urbanization. The results demonstrate that this hybrid approach enables more nuanced urban development while maintaining overall city functionality.

While state-of-the-art LLMs have shown poor logical and basic mathematical reasoning, recent works try to improve their problem-solving abilities using prompting techniques. We propose giving "hints" to improve the language model's performance on advanced mathematical problems, taking inspiration from how humans approach math pedagogically. We also test robustness to adversarial hints and demonstrate their sensitivity to them. We demonstrate the effectiveness of our approach by evaluating various diverse LLMs, presenting them with a broad set of problems of different difficulties and topics from the MATH dataset and comparing against techniques such as one-shot, few-shot, and chain of thought prompting.