Final answer:
The pain management task that can be safely delegated to nursing assistive personnel is providing a therapeutic back massage.
Step-by-step explanation:
The pain management task that can be safely delegated to nursing assistive personnel is providing a therapeutic back massage. Nursing assistive personnel, under the supervision of registered nurses or other healthcare professionals, can perform therapeutic back massages to help relieve pain and promote relaxation.
Assessing the quality and intensity of the patient's pain (option 1) and evaluating the effectiveness of pain medication (option 2) require knowledge and skills that are typically within the scope of registered nurses or advanced healthcare providers.
Administering an oral dose of acetaminophen (option 4) also requires careful medication administration and monitoring, making it less suitable for delegation to nursing assistive personnel.