LLM agents have become increasingly sophisticated, especially in the realm of cybersecurity. Researchers have shown that LLM agents can exploit real-world vulnerabilities when given a description of the vulnerability and toy capture-the-flag problems. However, these agents still perform poorly on real-world vulnerabilities that are unknown to the agent ahead of time (zero-day vulnerabilities).In this work, we show that teams of LLM agents can exploit real-world, zero-day vulnerabilities. Prior agents struggle with exploring many different vulnerabilities and long-range planning when used alone. To resolve this, we introduce HPTSA, a system of agents with a planning agent that can launch subagents. The planning agent explores the system and determines which subagents to call, resolving long-term planning issues when trying different vulnerabilities. We construct a benchmark of 14 real-world vulnerabilities and show that our team of agents improve over prior agent frameworks by up to 4.3×.