In this paper, the coevolution mechanism of trust-based partner switching among partitioned regions on an adaptive network is studied. We investigate a low-information approach to building trust and cooperation in public goods games. Unlike reputation, trust scores are only given to players by those with whom they have a relationship in the game, depending on the game they play together. A player's trust score for a certain neighbor is given and known by that player only. Players can adjust their connections to neighbors with low trust scores by switching their partners to other players. When switching partners, players divide other nodes in the network into three regions: immediate neighbors as the known region, indirectly connected second-order neighbors as the intermediate region, and other nodes as the unknown region. Such choices and compartmentalization often occur in global and regional economies. Our results show that preference for switching to partners in the intermediate region is not conducive to spreading cooperation, while random selection has the disadvantage of protecting the cooperator. However, selecting new partners in the remaining two regions based on the average trust score of the known region performs well in both protecting partners and finding potential cooperators. Meanwhile, by analyzing the parameters, we find that the influence of vigilance increasing against unsatisfactory behavior on evolution direction depends on the level of cooperation reward.