Which of the following actions allows a system to continue operating despite existing problems?

The correct choice is adaptive action. This action involves making adjustments or changes to a system in response to problems or changes in the environment that allow the system to continue functioning, albeit with some modifications or compromises. By adapting to the current circumstances, the system can maintain performance despite facing issues that could potentially hinder its original operation.

Adaptive action is essential in many engineering and operational contexts, where conditions can fluctuate or unforeseen challenges arise. This kind of action ensures that rather than ceasing operations due to difficulties, a system can find ways to adjust, whether through temporary solutions or strategic modifications.

The other options provide different approaches to managing issues. Permanent action may refer to fixed solutions that do not allow for flexibility. Interim action implies temporary measures, which might not offer long-term viability. Corrective action typically seeks to address and resolve specific problems rather than adapting to ongoing issues, thus focusing on returning to a previous state rather than continuing under new conditions.