Final answer:
The question relates to a patient on lithium carbonate showing signs of potential toxicity. The priority nursing action is to check the patient's blood lithium level to determine if toxicity is present.
Step-by-step explanation:
The question concerns a patient treated with lithium carbonate who is exhibiting symptoms that may suggest lithium toxicity, such as excessive thirst and slurred speech. These symptoms could indicate that the patient's blood lithium levels are too high. Therefore, the priority nursing action in this case would be c. Check the patient's blood lithium level. This is crucial because it will provide concrete evidence of whether the patient is experiencing lithium toxicity, and then appropriate measures such as adjusting the lithium dose or administering agents to reverse the toxicity can be taken.