Contextual information is vital for accurate trajectory prediction. For instance, the intricate flying behavior of migratory birds hinges on their analysis of environmental cues such as wind direction and air pressure. However, the diverse and dynamic nature of contextual information renders it an arduous task for AI models to comprehend its impact on trajectories and consequently predict them accurately. To address this issue, we propose a ``manager-worker'' framework to unleash the full potential of contextual information and construct CATP model, an implementation of the framework for Context-Aware Trajectory Prediction. The framework comprises a manager model, several worker models, and a tailored training mechanism inspired by competition symbiosis in nature. Taking CATP as an example, each worker needs to compete against others for training data and develop an advantage in predicting specific moving patterns. The manager learns the workers' performance in different contexts and selects the best one in the given context to predict trajectories, enabling CATP as a whole to operate in a symbiotic manner. We conducted two comparative experiments and an ablation study to quantitatively evaluate the proposed framework and CATP model. The results showed that CATP could outperform SOTA models, and the framework could be generalized to different context-aware tasks.