Final answer:
To identify Cullen's sign, the nurse should inspect the skin around the umbilicus as it indicates periumbilical bruising associated with severe pancreatitis.
Step-by-step explanation:
To identify Cullen's sign in a client who has pancreatitis, the appropriate action by the nurse would be to inspect the skin around the umbilicus. Cullen's sign is characterized by bruising in the periumbilical area, which may indicate intra-abdominal bleeding, potentially linked to severe pancreatitis. It is not related to tenderness at the costovertebral angle, abdominal palpation in a specific quadrant, or auscultation of the lungs.