Sharing tabular data in high-stakes domains is constrained by privacy regulations. Synthetic data offer a promising alternative, but deep generative models are costly to train and difficult to audit, while LLM-based methods often serialize records as text, obscuring tabular structure and exposing sensitive data. We introduce Tabular Synthesis Strategy Designer (TabSSD), which uses an LLM to design synthesis procedures rather than directly generate records. TabSSD provides the LLM with tree-derived summaries of variable dependence rather than raw records, which produces Python programs for local execution and evaluation. Across twelve datasets, TabSSD strikes a favourable balance among statistical fidelity, predictive utility, and empirical privacy risk, achieving the best average rank across six metrics among ten methods. Moreover, it substantially reduces local computation and token consumption relative to the compared methods. By enabling human-guided refinement and eliminating user-side model tuning, TabSSD lowers the expertise and infrastructure barriers to transparent tabular data synthesis.

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