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Ensuring reliable operation of large power systems subjected to multiple outages is a challenging task because of the combinatorial nature of the problem. Traditional approaches for security assessment are often limited by their scope and/or speed, resulting in missing of critical contingencies that could lead to cascading failures. This paper proposes a two-component methodology to enhance power system security. The first component combines an efficient algorithm to detect cut-set saturation (called the feasibility test (FT) algorithm) with real-time contingency analysis (RTCA) to create an integrated corrective action (iCA), whose goal is to secure the system against cut-set saturation as well as critical branch overloads. The second component only employs the results of the FT to create a relaxed corrective action (rCA) to secure the system against post-contingency cut-set saturation. The first component is more comprehensive, but the latter is computationally more efficient. The effectiveness of the two components is evaluated based upon the number of cascade triggering contingencies alleviated, and the computation time. The results obtained by analyzing different case-studies on the IEEE 118-bus and 2000-bus synthetic Texas systems indicate that the proposed two-component methodology successfully enhances the scope and speed of power system security assessment during multiple outages. [ABSTRACT FROM AUTHOR]