Adverse Drug Event (ADE) normalization to standardized medical terminologies such as MedDRA presents significant challenges due to lexical and semantic gaps between colloquial user-generated content and formal medical vocabularies. This paper presents our submission to the ALTA 2025 Shared Task on ADE normalization, evaluated using Accuracy@k metrics. Our approach employs distinct methodologies for the development and test phase. In the development phase, we propose a three-stage neural architecture: (1) bi-encoder training to establish semantic representations, (2) lexical-aware fine-tuning to capture morphological patterns alongside semantic similarity, and (3) crossencoder re-ranking for fine-grained discrimination, enabling the model to leverage both distributional semantics and lexical cues through explicit interaction modeling. For the test phase, we utilize the trained bi-encoder from stage (1) for efficient candidate retrieval, then adopt an alternative re-ranking pipeline leveraging large language models with tool-augmented retrieval and multi-stage reasoning. Specifically, a capable model performs reasoning-guided candidate selection over the retrieved top-k results, a lightweight model provides iterative feedback based on reasoning traces, and an automated verification module ensures output correctness with self-correction mechanisms. Our system achieves competitive performance on both development and test benchmarks, demonstrating the efficacy of neural retrieval-reranking architectures and the versatility of LLM-augmented neural pipelines for medical entity normalization tasks.