Final answer:
The nurse should inspect the patient's sclera, nail beds, and conjunctiva of the eyes for cyanosis.
Step-by-step explanation:
The nurse should inspect the patient's sclera, nail beds, and conjunctiva of the eyes for cyanosis. Cyanosis is the bluish discoloration of the skin and mucous membranes caused by a lack of oxygen in the blood. Inspecting these areas can help the nurse assess the patient's oxygenation status.