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As the Web transitions from static retrieval to generative interaction, the escalating environmental footprint of Large Language Models (LLMs) presents a critical sustainability challenge. Current paradigms indiscriminately apply computation-intensive strategies like Chain-of-Thought (CoT) to billions of daily queries, causing LLM overthinking, a redundancy that amplifies carbon emissions and operational barriers. This inefficiency directly undermines UN Sustainable Development Goals 13 (Climate Action) and 10 (Reduced Inequalities) by hindering equitable AI access in resource-constrained regions. To address this, we introduce EcoThink, an energy-aware adaptive inference framework designed to reconcile high-performance AI intelligence with environmental responsibility. EcoThink employs a lightweight, distillation-based router to dynamically assess query complexity, skipping unnecessary reasoning for factoid retrieval while reserving deep computation for complex logic. Extensive evaluations across 9 diverse benchmarks demonstrate that EcoThink reduces inference energy by 40.4% on average (up to 81.9% for web knowledge retrieval) without statistically significant performance loss. By mitigating algorithmic waste, EcoThink offers a scalable path toward a sustainable, inclusive, and energy-efficient generative AI Agent.