Final answer:
The appropriate initial action is to report the incident immediately to the nurse manager or nursing supervisor.
Step-by-step explanation:
The appropriate initial action for the second nurse in this situation is to report the incident immediately to the nurse manager or nursing supervisor.
Reporting this incident is necessary as it involves a potential breach in the medication handling process, which could compromise patient safety. The nurse who was asked to sign for the wasted narcotic did not witness the waste, raising concerns about medication security and proper documentation.
By reporting the situation, the nurse ensures that the incident is properly documented and investigated, allowing for appropriate actions to be taken to prevent any further risks or potential drug diversion.