Recent advances in LLM-based agents highlight the importance of their reasoning frameworks, which guide the problem-solving process in diverse ways. This survey introduces a unified formal language to systematically categorize these frameworks at three compositional levels: single-agent, tool-based, and multi-agent methods. Following our taxonomy, we review key application scenarios across scientific discovery, healthcare, software engineering, society, economics, and general-purpose tasks. It also compares the distinct features and evaluation strategies of each category. Through our taxonomy and comparisons, our survey explores the designs and strengths of LLM-based agentic frameworks in different scenarios, reviewing the fast-paced development of complex agentic systems in the real world.

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