Coaches are vital for effective collaboration, but cost and resource constraints often limit their availability during real-world tasks. This limitation poses serious challenges in life-critical domains that rely on effective teamwork, such as healthcare and disaster response. To address this gap, we propose and realize an innovative application of AI: task-time team coaching. Specifically, we introduce Socratic, a novel AI system that complements human coaches by providing real-time guidance during task execution. Socratic monitors team behavior, detects misalignments in team members' shared understanding, and delivers automated interventions to improve team performance. We validated Socratic through two human subject experiments involving dyadic collaboration. The results demonstrate that the system significantly enhances team performance with minimal interventions. Participants also perceived Socratic as helpful and trustworthy, supporting its potential for adoption. Our findings also suggest promising directions both for AI research and its practical applications to enhance human teamwork.