Creativity involves not only generating new ideas from scratch but also redefining existing concepts and synthesizing previous insights. Among various techniques developed to foster creative thinking, brainstorming is widely used. With recent advancements in Large Language Models (LLMs), tools like ChatGPT have significantly impacted various fields by using prompts to facilitate complex tasks. While current research primarily focuses on generating accurate responses, there is a need to explore how prompt engineering can enhance creativity, particularly in brainstorming. Therefore, this study addresses this gap by proposing a framework called GPS, which employs goals, prompts, and strategies to guide designers to systematically work with an LLM tool for improving the creativity of ideas generated during brainstorming. Additionally, we adapted the Torrance Tests of Creative Thinking (TTCT) for measuring the creativity of the ideas generated by AI. Our framework, tested through a design example and a case study, demonstrates its effectiveness in stimulating creativity and its seamless LLM tool integration into design practices. The results indicate that our framework can benefit brainstorming sessions with LLM tools, enhancing both the creativity and usefulness of generated ideas.