Large Language Models (LLMs) have demonstrated impressive capabilities, yet their deployment in high-stakes domains is hindered by inherent limitations in trustworthiness, including hallucinations, instability, and a lack of transparency. To address these challenges, we introduce a generic neuro-symbolic approach, which we call Autonomous Trustworthy Agents (ATA). The core of our approach lies in decoupling tasks into two distinct phases: Offline knowledge ingestion and online task processing. During knowledge ingestion, an LLM translates an informal problem specification into a formal, symbolic knowledge base. This formal representation is crucial as it can be verified and refined by human experts, ensuring its correctness and alignment with domain requirements. In the subsequent task processing phase, each incoming input is encoded into the same formal language. A symbolic decision engine then utilizes this encoded input in conjunction with the formal knowledge base to derive a reliable result. Through an extensive evaluation on a complex reasoning task, we demonstrate that a concrete implementation of ATA is competitive with state-of-the-art end-to-end reasoning models in a fully automated setup while maintaining trustworthiness. Crucially, with a human-verified and corrected knowledge base, our approach significantly outperforms even larger models, while exhibiting perfect determinism, enhanced stability against input perturbations, and inherent immunity to prompt injection attacks. By generating decisions grounded in symbolic reasoning, ATA offers a practical and controllable architecture for building the next generation of transparent, auditable, and reliable autonomous agents.