LLMs have demonstrated strong performance in data-rich domains such as programming, yet their reliability in engineering tasks remains limited. Circuit analysis--requiring multimodal understanding and precise mathematical reasoning--highlights these challenges. Although Gemini 2.5 Pro shows improved capabilities in diagram interpretation and analog-circuit reasoning, it still struggles to consistently produce correct solutions when given both textual problem descriptions and circuit diagrams. Meanwhile, engineering education demands scalable AI tools capable of generating accurate solutions for applications such as automated homework feedback. This paper presents an enhanced end-to-end circuit problem-solving framework built upon Gemini. We first conduct a systematic benchmark on undergraduate circuit problems and identify two key failure modes: 1) circuit-recognition hallucinations, particularly incorrect source polarity detection, and 2) reasoning-process hallucinations, such as incorrect current direction assumptions. To address recognition errors, we integrate a fine-tuned YOLO detector and OpenCV-based processing to isolate voltage and current sources, enabling Gemini to accurately re-identify source polarities from cropped images. To mitigate reasoning errors, we introduce an ngspice-driven verification loop, in which simulation discrepancies trigger iterative solution refinement with optional HITL feedback. Experimental results demonstrate that the proposed pipeline achieves 97.59% accuracy, substantially outperforming Gemini's baseline of 79.52%. Furthermore, on four variations of hand-drawn circuit diagrams, accuracy improves from 56.06%--71.21% to 93.94%--95.45% with statistically significant gains. These results highlight the robustness, scalability, and practical applicability of the proposed framework for engineering education and real-world circuit analysis tasks.