Final answer:
The nurse's first action should be to assess the client's vital signs when a medication error is discovered. Following the assessment, notifying the physician and documenting the incident are necessary steps. Apologies to the client and family come after ensuring the client's safety.
Step-by-step explanation:
When a nurse discovers that a client diagnosed with dementia has received the wrong medication, the nurse's first action should be to assess the client's vital signs. This is critical to ensure that the client is stable and to determine the immediate impact of the error. After assessing and stabilizing the client, the nurse should then notify the physician responsible for the care of the client to inform them of the error and discuss the next steps. Additionally, it is important to document the incident in the client's medical records, including the details of the wrong medication given, the assessment findings, and any actions taken following the discovery. Finally, apologizing to the client and family may be appropriate, but this should occur after the immediate medical concerns have been addressed.