Recommender systems have achieved increasing accuracy over the years. However, this precision often leads users to narrow their interests, resulting in issues such as limited diversity and the creation of echo chambers. Current research addresses these challenges through proactive recommender systems by recommending a sequence of items (called influence path) to guide user interest in the target item. However, existing methods struggle to construct a coherent influence path that builds up with items the user is likely to enjoy. In this paper, we leverage the Large Language Model's (LLMs) exceptional ability for path planning and instruction following, introducing a novel approach named LLM-based Influence Path Planning (LLM-IPP). Our approach maintains coherence between consecutive recommendations and enhances user acceptability of the recommended items. To evaluate LLM-IPP, we implement various user simulators and metrics to measure user acceptability and path coherence. Experimental results demonstrate that LLM-IPP significantly outperforms traditional proactive recommender systems. This study pioneers the integration of LLMs into proactive recommender systems, offering a reliable and user-engaging methodology for future recommendation technologies.