Automated tools for video editing and assembly have applications ranging from filmmaking and advertisement to content creation for social media. Previous video editing work has mainly focused on either retrieval or user interfaces, leaving actual editing to the user. In contrast, we propose to automate the core task of video editing, formulating it as sequential decision making process. Ours is a multi-agent approach. We design an Editor agent and a Critic agent. The Editor takes as input a collection of video clips together with natural language instructions and uses tools commonly found in video editing software to produce an edited sequence. On the other hand, the Critic gives natural language feedback to the editor based on the produced sequence or renders it if it is satisfactory. We introduce a learning-based approach for enabling effective communication across specialized agents to address the language-driven video editing task. Finally, we explore an LLM-as-a-judge metric for evaluating the quality of video editing system and compare it with general human preference. We evaluate our system's output video sequences qualitatively and quantitatively through a user study and find that our system vastly outperforms existing approaches in terms of coverage, time constraint satisfaction, and human preference.