Final answer:
The nurse should first set the infusion pump for the correct infusion rate.
Step-by-step explanation:
The action that the nurse should take first when caring for a client with cardiogenic shock who has been prescribed dobutamine infusion is to set the infusion pump for the correct infusion rate. This is essential to ensure that the medication is administered at the appropriate dosage and rate. While comparing the packaging of the medication to the prescription, priming the IV tubing with the medication, and increasing the frequency of blood pressure and heart rate monitoring are all important actions, setting the infusion pump correctly takes priority to ensure the patient's safety and effective treatment.