We present and discuss a fully-automated collaboration system, CoCo, that allows multiple participants to video chat and receive feedback through custom video conferencing software. After a conferencing session, a virtual feedback assistant provides insights on the conversation to participants. CoCo automatically pulls audial and visual data during conversations and analyzes the extracted streams for affective features, including smiles, engagement, attention, as well as speech overlap and turn-taking. We validated CoCo with 39 participants split into 10 groups. Participants played two back-to-back team-building games, Lost at Sea and Survival on the Moon, with the system providing feedback between the two. With feedback, we found a statistically significant change in balanced participation---that is, everyone spoke for an equal amount of time. There was also statistically significant improvement in participants' self-evaluations of conversational skills awareness, including how often they let others speak, as well as of teammates' conversational skills. The entire framework is available at https://github.com/ROC-HCI/CollaborationCoach_PostFeedback.