Final answer:
The phlebotomy technician should have the patient rest for at least 15 minutes before the venipuncture.
Step-by-step explanation:
The correct precautionary action for the phlebotomy technician to take when the patient states that he ran to the facility before the venipuncture is to have the patient rest comfortably for at least 15 min before the venipuncture.
This is because strenuous activity, such as running, can affect the body's physiology and potentially lead to changes in blood composition, such as elevated levels of certain analytes. By allowing the patient to rest for 15 minutes, the body can have a chance to return to a more stable state, reducing the risk of obtaining inaccurate or abnormal results from the blood sample.