Multi-access point coordination (MAPC) is a key technology for enhancing throughput in next-generation Wi-Fi within dense overlapping basic service sets. However, existing MAPC protocols rely on static, protocol-defined rules, which limits their ability to adapt to dynamic network conditions such as varying interference levels and topologies. To address this limitation, we propose a novel Agentic AI Wi-Fi framework where each access point, modeled as an autonomous large language model agent, collaboratively reasons about the network state and negotiates adaptive coordination strategies in real time. This dynamic collaboration is achieved through a cognitive workflow that enables the agents to engage in natural language dialogue, leveraging integrated memory, reflection, and tool use to ground their decisions in past experience and environmental feedback. Comprehensive simulation results demonstrate that our agentic framework successfully learns to adapt to diverse and dynamic network environments, significantly outperforming the state-of-the-art spatial reuse baseline and validating its potential as a robust and intelligent solution for future wireless networks.