Large language models (LLMs) are increasingly deployed as autonomous agents in multi-agent systems, yet their ability to reliably execute distributed coordination protocols remains poorly understood. While AgentsNet, a benchmark framework for distributed coordination among LLM agents, enables such coordination, granting full reasoning autonomy often leads to inconsistent or degraded performance in complex domains. We hypothesize that coordination can be improved by regulating agent autonomy through symbolic guidance derived from established algorithms. To investigate this, we introduce the \emph{Symbolic Guidance Taxonomy (SGT)}, which characterizes a spectrum of autonomy ranging from open-ended natural language reasoning to fully prescribed algorithmic execution, with intermediate levels providing partial pseudocode guidance. Our results show that intermediate autonomy levels consistently outperform both unguided agents and fully prescriptive specifications. These findings identify autonomy regulation as a key design principle for LLM-based distributed coordination.

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