Final answer:
The safe nursing action would be to inform the healthcare provider and document the incident.
Step-by-step explanation:
The safe nursing action in this situation would be option c) Inform the healthcare provider and document the incident.
When a nurse accidentally drops a syringe on the floor, it is considered contaminated and should not be reused or administered to a client. This is to prevent the risk of introducing pathogens into the client's body. Therefore, the nurse should discard the syringe and prepare a new one to administer the medication safely.