The paper presents our system developed for SemEval-2025 Task 8, which focuses on table question answering (TQA). The TQA tasks face challenges due to the characteristics of real-world tabular data, such as large size, incomplete column semantics, and entity ambiguity. To address these issues, we propose a large language model (LLM)-powered and programming-based framework, named Flow-of-Table-Reasoning. We introduce the table schema integrating verbalized structure and semantics for query decomposition and programming, enabling a holistic understanding of tables and the ability to process large-size tables. We design a multi-step schema linking plan to derive a focused table schema that retains only information relevant to the query, aiming to eliminate ambiguity and reduce hallucinations. Furthermore, we incorporate reasoning workflow into an iterative thinking architecture, allowing incremental cycles of thinking, reasoning and reflection. Our system achieves first place on both TQA and Lite TQA subtasks.