Mining and conveying actionable insights from complex data is a key challenge of exploratory data analysis (EDA) and storytelling. To address this challenge, we present a design space for actionable EDA and storytelling. Synthesizing theory and expert interviews, we highlight how semantic precision, rhetorical persuasion, and pragmatic relevance underpin effective EDA and storytelling. We also show how this design space subsumes common challenges in actionable EDA and storytelling, such as identifying appropriate analytical strategies and leveraging relevant domain knowledge. Building on the potential of LLMs to generate coherent narratives with commonsense reasoning, we contribute Jupybara, an AI-enabled assistant for actionable EDA and storytelling implemented as a Jupyter Notebook extension. Jupybara employs two strategies -- design-space-aware prompting and multi-agent architectures -- to operationalize our design space. An expert evaluation confirms Jupybara's usability, steerability, explainability, and reparability, as well as the effectiveness of our strategies in operationalizing the design space framework with LLMs.