We introduce a multi-step reasoning framework using promptbased LLMs to examine the relationship between social media language patterns and trends in national health outcomes. Grounded in fuzzy-trace theory, which emphasizes the importance of "gists" of causal coherence in effective health communication, we introduce Role-Based Incremental Coaching (RBIC), a prompt-based LLM framework, to identify gists at-scale. Using RBIC, we systematically extract gists from subreddit discussions opposing COVID-19 health measures (Study 1). We then track how these gists evolve across Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s).