This work proposes a data-informed approach for an adaptable coordination of damping controllers. The novel concept of coordination is based on minimizing the Total Action, a single metric that measures the system's dynamic response postdisturbance. This is a performance measure based on the physics of the power system, which encapsulates the oscillation energy related to synchronous generators. Deep learning theory is used to propose a Total Action function approximator, which captures the relationship between the system wide-area measurements, the status of damping controllers, and the conditions of the disturbance. By commissioning the switching status (on/off) of damping controllers in real-time, the oscillation energy is reduced, enhancing the power system stability. The concept is tested in the Western North America Power System (wNAPS) and compared with a model-based approach for the coordination of damping controllers. The data-informed coordination outperforms the model-based approach, demonstrating exceptional adaptability and performance to handle multi-modal events. The proposed scheme shows outstanding reductions in lowfrequency oscillations even under various operating conditions, fault locations, and time delay considerations.