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Process mining provides powerful insights into organizational workflows, but extracting these insights typically requires expertise in specialized query languages and data science tools. Large Language Models (LLMs) offer the potential to democratize process mining by enabling business users to interact with process data through natural language. However, using LLMs as direct analytical engines over raw event logs introduces fundamental challenges: LLMs struggle with deterministic reasoning and may hallucinate metrics, while sending large, sensitive logs to external AI services raises serious data-privacy concerns. To address these limitations, we present PMAx, an autonomous agentic framework that functions as a virtual process analyst. Rather than relying on LLMs to generate process models or compute analytical results, PMAx employs a privacy-preserving multi-agent architecture. An Engineer agent analyzes event-log metadata and autonomously generates local scripts to run established process mining algorithms, compute exact metrics, and produce artifacts such as process models, summary tables, and visualizations. An Analyst agent then interprets these insights and artifacts to compile comprehensive reports. By separating computation from interpretation and executing analysis locally, PMAx ensures mathematical accuracy and data privacy while enabling non-technical users to transform high-level business questions into reliable process insights.