Inspired by human cognition, Jiang et al.(2023c) create a benchmark for assessing LLMs' lateral thinking-thinking outside the box. Building upon this benchmark, we investigate how different prompting methods enhance LLMs' performance on this task to reveal their inherent power for outside-the-box thinking ability. Through participating in SemEval-2024, task 9, Sentence Puzzle sub-task, we explore prompt engineering methods: chain of thoughts (CoT) and direct prompting, enhancing with informative descriptions, and employing contextualizing prompts using a retrieval augmented generation (RAG) pipeline. Our experiments involve three LLMs including GPT-3.5, GPT-4, and Zephyr-7B-beta. We generate a dataset of thinking paths between riddles and options using GPT-4, validated by humans for quality. Findings indicate that compressed informative prompts enhance performance. Dynamic in-context learning enhances model performance significantly. Furthermore, fine-tuning Zephyr on our dataset enhances performance across other commonsense datasets, underscoring the value of innovative thinking.