Final answer:
A train operator given permission to move past a red automatic signal with a "K" sign must proceed with extreme caution and at a reduced speed, following the specific regulations and safety protocols.
Step-by-step explanation:
When a train operator is given permission to move past a red automatic signal with a "K" sign, specific procedures must be followed according to railway regulations and safety protocols. In most cases, being allowed to proceed after stopping at a red signal indicates an exceptional situation, possibly due to signal failure or when the route is known to be clear despite the red indication. The operator must proceed with extreme caution, at a reduced speed, and be ready to stop if an obstruction is detected on the tracks. Additionally, there may be specific rules that come with the "K" sign designation, meaning that the operator must be fully aware of the railway's code of operations.
The precise steps may vary by region and rail company but generally involve a combination of verbal or written authority, acknowledgment of understanding, and confirmation of the clearness of the track ahead. It's crucial for the safety of everyone involved that train operators adhere strictly to these guidelines when encountering such signals.