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The active safety systems available in passenger cars today automatically deploy automated safety interventions in situations where the driver is in need of assistance. In this paper, we consider the process of determining whether such interventions are needed. In particular, we design a threat assessment method that evaluates the risk that the vehicle will either leave the road or its maneuverability will be significantly reduced within a finite time horizon. The proposed threat assessment method accounts for combined braking and steering maneuvers, which results in a nonlinear dynamical vehicle behavior. We formulate the threat assessment problem as a nonconvex constraint satisfaction problem (CSP) and implement an algorithm that solves it through interval-based consistency techniques. Experimental validation of the proposed approach indicates that constraint violation can be predicted while avoiding the detection of false threats.