Final answer:
The trackman should inform the supervisor about the badly worn rail for proper assessment and action, ensuring safety protocol is followed.
Step-by-step explanation:
If a trackman discovers a badly worn rail, the correct action to take is to inform the supervisor. It is the responsibility of the supervisor to assess the situation and determine the appropriate course of action, which may include replacing or repairing the rail.
The trackman should not attempt to repair or replace the rail themselves unless they have been trained and are authorized to do so. Ignoring a worn rail could lead to serious safety hazards such as derailments.