The "black box" nature of Large Reasoning Models (LRMs) presents critical limitations in reliability and transparency, fueling the debate around the "illusion of thinking" and the challenge of state hallucinations in agentic systems. In response, we introduce The STAR-XAI Protocol (Socratic, Transparent, Agentic, Reasoning - for eXplainable Artificial Intelligence), a novel operational methodology for training and operating verifiably reliable AI agents. Our method reframes the human-AI interaction as a structured Socratic dialogue governed by an explicit, evolving symbolic rulebook (the Consciousness Transfer Package - CTP) and a suite of integrity protocols, including a state-locking Checksum that eradicates internal state corruption. Through an exhaustive case study in the complex strategic game "Caps i Caps," we demonstrate that this "Clear Box" framework transforms an opaque LRM into a disciplined strategist. The agent not only exhibits the emergence of complex tactics, such as long-term planning, but also achieves ante-hoc transparency by justifying its intentions before acting. Crucially, it demonstrates Second-Order Agency by identifying and correcting flaws in its own supervisor-approved plans, leading to empirically-proven, 100% reliable state tracking and achieving "zero hallucinations by design." The STAR-XAI Protocol thus offers a practical pathway toward building AI agents that are not just high-performing but intrinsically auditable, trustworthy, and reliable.