SQL languages often feature nested structures that require robust interaction with databases. Aside from the well-validated schema linking methods on PLMs and LLMs, we introduce the Linearly Incremental SQL Translator (LIST), a novel algorithmic toolkit designed to leverage the notable reasoning and tool interaction capabilities inherent in LLMs. LIST transforms complex SQL queries into grammatically verifiable sub-queries which are arranged sequentially to reflect single-hop reasoning steps, enhancing both the granularity and accuracy of database interactions. With in-context learning, our experiments demonstrated significant improvements, achieving notable performance of 60.56% and 56.32% on the BIRD dataset with GPT-4o and Llama-3-70B-Instruct. To the best of our knowledge, this achieves SOTA performance among non-schema linking methods, also surpassing a series of schema linking based approaches at a comparable or better cost.