The era of the Internet of Agents (IoA) is taking shape: LLM agents are expected to fulfill user goals by orchestrating fast-growing populations of Model Context Protocol (MCP) servers, Agent-to-Agent (A2A) endpoints, reusable skills, and other LLM-callable services. Yet LLMs face a structural mismatch with this regime: effective context is a scarce resource that does not scale with the number of services. Concatenating thousands of service descriptions into a prompt overflows the context window, and even when the window is large enough, models systematically under-attend to information in the middle of long inputs, the well-documented Lost-in-the-Middle phenomenon. This is fundamentally a question of context management for service discovery. To address this, we propose an LLM-native progressive-disclosure scheme and its concrete instantiation, A2X (Agent-to-Anything service discovery): an LLM-driven pipeline that automatically organizes the registered services into a hierarchical taxonomy and walks it layer by layer at query time, so that every LLM call sees only a small candidate set highly relevant to the user query. This decouples effective-context scarcity from registry size and significantly reduces token consumption while improving retrieval accuracy. Compared to full-context dumping, A2X achieves a 6.2-point Hit Rate gain at one-ninth the prompt-token cost; compared to the state-of-the-art open-source embedding-based baseline, A2X improves Hit Rate by more than 20 points.