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This paper deals with day-ahead power systems security planning under uncertainties by posing an optimization problem over a set of power injection scenarios that could show up the next day and modeling the next day's real-time control strategies aiming at ensuring security with respect to contingencies by a combination of preventive and corrective controls. We seek to determine whether and which day-ahead decisions must be taken so that, for scenarios over the next day, there still exists an acceptable combination of preventive and corrective controls ensuring system security for any postulated contingency. We formulate this task as a three-stage feasibility checking problem, where the first stage corresponds to day-ahead decisions, the second stage to preventive control actions, and the third stage to corrective post-contingency controls. We propose a solution approach based on the problem decomposition into successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. Our approach is illustrated on the Nordic32 system and on a 1203-bus model of a real-life system.