The method includes installing a system for inspecting the core shroud on the core shroud, driving the system horizontally around the core shroud, and using a sensor of the system to inspect the core shroud, where the system includes a trolley, an arm, a tether, and a remotely operated vehicle (ROV) for inspecting the core shroud. The ROV includes a body configured to be operatively connected to the tether, and the sensor is configured to be operatively connected to the body, and configured to provide inspection information of the core shroud. The arm is configured to be operatively connected to the trolley. The ROV is configured to be operatively connected to the arm via the tether, and the tether is configured to provide vertical position information for the ROV relative to the outer surface of the core shroud.