To smoothly and efficiently enable autonomous mobile robots to move in human crowd environments, path planning based on human movement-prediction, reactive movement toward human movement, and active motion-inducing physical interaction to avoid getting stuck are required. In this study, we developed a reactive, proactive, and inducible proximal crowd navigation (PCN) method that is based on a newly developed inducible social force model (${\boldsymbol{i}}$-SFM). The PCN first reactively generates multiple paths including avoidance, proximal, and inducible physical-touch paths based on the waypoint-${\boldsymbol{i}}$-SFM fused-path planning method, proactively predicts human movement based on ${\boldsymbol{i}}$-SFM, selects an optimal path based on the movement cost including robot-movement efficiency and the crowd-invasion index (impulsive and touch forces applied to the humans), and finally reactively moves in the crowd based on the forces applied on it. The proposed PCN method works not only when the robot enters crowds but also when it is already in a crowd and avoids humans who enter the crowd, so we also applied our PCN method to both situations. Simulation and experimental results indicated that our PCN method can adequately predict the movement of human crowds and achieve higher movement efficiency without stuck, compared with a conventional non-proximal navigation methodusing the SFM.