At present, Connected Autonomous Vehicles (CAVs) have begun to open road testing around the world, but their safety and efficiency performance in complex scenarios is still not satisfactory. Cooperative driving leverages the connectivity ability of CAVs to achieve synergies greater than the sum of their parts, making it a promising approach to improving CAV performance in complex scenarios. However, the lack of interaction and continuous learning ability limits current cooperative driving to single-scenario applications and specific Cooperative Driving Automation (CDA). To address these challenges, this paper proposes CoDrivingLLM, an interactive and learnable LLM-driven cooperative driving framework, to achieve all-scenario and all-CDA. First, since Large Language Models(LLMs) are not adept at handling mathematical calculations, an environment module is introduced to update vehicle positions based on semantic decisions, thus avoiding potential errors from direct LLM control of vehicle positions. Second, based on the four levels of CDA defined by the SAE J3216 standard, we propose a Chain-of-Thought (COT) based reasoning module that includes state perception, intent sharing, negotiation, and decision-making, enhancing the stability of LLMs in multi-step reasoning tasks. Centralized conflict resolution is then managed through a conflict coordinator in the reasoning process. Finally, by introducing a memory module and employing retrieval-augmented generation, CAVs are endowed with the ability to learn from their past experiences. We validate the proposed CoDrivingLLM through ablation experiments on the negotiation module, reasoning with different shots experience, and comparison with other cooperative driving methods.