In interdependent systems, such as electric power systems, entities or components mutually depend on each other. Due to these interdependencies, a small number of initial failures can propagate throughout the system, resulting in catastrophic system failures. This paper addresses the problem of finding the set of entities whose failures will have the worst effects on the system. To this end, a two-phase algorithm is developed. In the first phase, the tight bound on failure propagation steps is computed using a Boolean Satisfiablility (SAT) solver. In the second phase, the problem is formulated as an Integer Linear Programming (ILP) problem using the obtained step bound and solved with an ILP solver. Experimental results show that the algorithm scales to large problem instances and outperforms a single-phase algorithm that uses a loose step bound.