Final answer:
The first action the nurse should take is obtaining the client's vital signs to assess immediate stability and hemodynamic status. This is vital in a situation where the client is vomiting blood and could be at risk of hypovolemic shock.
Step-by-step explanation:
A nurse caring for a client with portal hypertension who is vomiting blood needs to prioritize interventions. When dealing with a potentially life-threatening situation such as hematemesis (vomiting blood), the primary concern is the client's immediate stability. The nursing action to take first is obtaining vital signs.
Vital signs provide critical information about the client's hemodynamic status and can indicate the severity of the blood loss and whether the client is in hypovolemic shock. Only after the initial assessment with vital signs can the nurse proceed with other actions such as checking laboratory values, establishing IV access for a potential transfusion, and obtaining a stat platelet count, in that order, based on the client's stability and hospital protocols.