The integration of Large Language Models (LLMs) into scientific research promises to accelerate discovery, yet a significant gap remains between the dynamic reasoning of Artificial Intelligence (AI) agents and the static, deterministic nature of canonical scientific workflows. This paper introduces ADEPT (Agentic Discovery and Exploration Platform for Tools), a reference architecture and pedagogical framework explicitly designed to bridge this gap. ADEPT's primary mission is to provide a transparent, "glass-box" environment where researchers and engineers can learn to effectively wrap established scientific software (e.g., BLAST, Nextflow pipelines) and compose it into reliable, agent-driven workflows. We describe its modular, multi-server architecture, which leverages the Model Context Protocol (MCP) for tool serving, LangGraph for robust agentic orchestration, and a secure nsjail-based sandbox for safe code execution. By prioritizing architectural clarity, safety, and modularity, ADEPT serves as an extensible blueprint for building trustworthy AI-augmented systems and fosters the collaborative development necessary to responsibly employ agentic AI for science. We provide practical examples of how to adapt and extend this framework, highlighting its utility in workforce development and AI-readiness capabilities across research and development projects.