Final answer:
The best action to take if a coworker asks you to sign his name on a patient chart he forgot to sign is to contact your supervisor or appropriate authority and report the situation to ensure legal and ethical practice.
Step-by-step explanation:
If a coworker calls from home and asks you to sign his name on a patient chart that he forgot to sign when administering a medication, the correct course of action is to refuse to sign your coworker's name, as this is both unethical and illegal. It could also lead to serious legal consequences for both you and your coworker, and it compromises patient care integrity. The most appropriate action to take would be option c) Contact your supervisor or appropriate authority to report the situation. By doing so, you ensure that the situation is dealt with legally and ethically, and the patient's care documentation remains accurate and trustworthy.