Final answer:
The best immediate action is to apply the brakes in emergency and then reduce speed gradually.
Step-by-step explanation:
The best immediate action for the train operator to take in this situation is to apply the brakes in emergency and then reduce speed gradually. Applying the brakes in emergency will help to stop the train quickly and prevent any potential collision with the broken rail. Once the train has slowed down, the operator can then take further actions such as contacting the railway maintenance team to repair the broken rail.