Mitigating climate change requires widespread behavior change. However, even climate-concerned individuals often hold misperceptions about which actions most effectively reduce carbon emissions. We recruited 1204 climate-concerned participants to examine whether discussing climate actions with a large language model (LLM) equipped with climate knowledge and tailored to provide personalized responses would promote more accurate impact perceptions and greater intentions to engage in high-impact behaviors, compared to using web search, a default LLM, or no intervention. The results show that participants in the personalized LLM condition produced more accurate impact assessments than those in the control and default LLM conditions, but did not differ from web search. However, the personalized LLM also increased intentions to perform high-impact behaviors relative to both the control and web search. The findings suggest that while LLMs might not outperform web searches in improving knowledge of climate action impacts, their ability to deliver personalized, actionable responses might more effectively motivate impactful pro-climate behavior change.