This paper presents a set of strategies to solve global behavioral properties of Petri nets. We introduce efficient methods to compute structural invariants and bounds, and to decide presence of stable places for both PT nets and colored nets. Our focus is on proposing strategies that scale to very large nets, even if precision is degraded or the test is only a semi-decision (e.g. a sufficient condition). These strategies form the decision procedures of ITS-Tools, that has won the annual model-checking competition MCC in these categories in both 2021 and 2022.