Recent research shows that greater numbers of people are turning to Large Language Models (LLMs) for emotional support, and that people rate LLM responses as more empathic than human-written responses. We suggest a reason for this success: LLMs have learned and consistently deploy a well-liked template for expressing empathy. We develop a taxonomy of 10 empathic language "tactics" that include validating someone's feelings and paraphrasing, and apply this taxonomy to characterize the language that people and LLMs produce when writing empathic responses. Across a set of 2 studies comparing a total of n = 3,265 AI-generated (by six models) and n = 1,290 human-written responses, we find that LLM responses are highly formulaic at a discourse functional level. We discovered a template -- a structured sequence of tactics -- that matches between 83--90% of LLM responses (and 60--83\% in a held out sample), and when those are matched, covers 81--92% of the response. By contrast, human-written responses are more diverse. We end with a discussion of implications for the future of AI-generated empathy.

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