How can an AI teammate implicitly coordinate with a human? We address this question by integrating Instance-Based Learning (IBL), a cognitive theory of learning and decision making, with the level-k Theory of Mind framework. We hypothesize that coordination emerges when partners adopt complementary k-levels and when the higher k-level agent has an accurate model of their partner's cognitive processes. To test this hypothesis, we introduce a simultaneous-choice, multi-attribute task, where outcomes depend on interactions between choice features and agent decisions. Simulations of pairs of IBL-based agents at different k-levels support the hypothesis that complementary k-levels enhance coordination. However, empirical results from an experiment reveal no advantage of human, IBL-L2 pairs over human, IBL-L1 pairs, even when participants are restricted to operate as L1 agents. Post-hoc simulations show that model fitting recovers some advantage for human, IBL-L2 teams by enabling the IBL-L2 agent to more accurately predict their human partner's actions.