The router that runs OSPF first enters the Full state and then synchronizes the LSDB.

Comprehensive Explanation: In OSPF (Open Shortest Path First), a router first synchronizes its Link-State Database (LSDB) with its neighbors by exchanging link-state information. Only after this synchronization process is complete does the router transition to the Full state. The Full state indicates that the router has fully converged with its OSPF neighbors and has a complete and up-to-date view of the network topology. Therefore, the router enters the Full state after synchronizing its LSDB, not before.