Large language models (LLM) based end-to-end task-oriented dialog (TOD) systems built using few-shot (in-context) learning perform better than supervised models only when the train data is limited. This is due to the inherent ability of LLMs to learn any task with just a few demonstrations. As the number of train dialogs increases, supervised SoTA models surpass in-context learning LLMs as they learn to better align with the style of the system responses in the training data, which LLMs struggle to mimic. In response, we propose SyncTOD, which synergizes LLMs with useful hints about the task for improved alignment. At a high level, SyncTOD trains auxiliary models to provide these hints and select exemplars for the in-context prompts. With ChatGPT, SyncTOD achieves superior performance compared to LLM-based baselines and SoTA models in low-data settings, while retaining competitive performance in full-data settings