Bounded model checking (BMC) and fuzzing techniques are among the most effective methods for detecting errors and security vulnerabilities in software. However, there are still shortcomings in detecting these errors due to the inability of existent methods to cover large areas in target code. We propose FuSeBMC v4, a test generator that synthesizes seeds with useful properties, that we refer to as smart seeds, to improve the performance of its hybrid fuzzer thereby achieving high C program coverage. FuSeBMC works by first analyzing and incrementally injecting goal labels into the given C program to guide BMC and Evolutionary Fuzzing engines. After that, the engines are employed for an initial period to produce the so-called smart seeds. Finally, the engines are run again, with these smart seeds as starting seeds, in an attempt to achieve maximum code coverage / find bugs. During both seed generation and normal running, coordination between the engines is aided by the Tracer subsystem. This subsystem carries out additional coverage analysis and updates a shared memory with information on goals covered so far. Furthermore, the Tracer evaluates test cases dynamically to convert cases into seeds for subsequent test fuzzing. Thus, the BMC engine can provide the seed that allows the fuzzing engine to bypass complex mathematical guards (e.g., input validation). As a result, we received three awards for participation in the fourth international competition in software testing (Test-Comp 2022), outperforming all state-of-the-art tools in every category, including the coverage category.