Final answer:
Providing a therapeutic back massage can be safely delegated to nursing assistive personnel, while tasks like assessing pain and evaluating pain medication effectiveness, as well as administering medications, should be done by licensed nursing staff.
Step-by-step explanation:
The pain management task that can be safely delegated to nursing assistive personnel (NAP) is providing a therapeutic back massage. Assessing the quality and intensity of a patient's pain and evaluating the effectiveness of pain medication are tasks that require clinical judgment and therefore should be performed by a licensed nurse. Administering an oral dose of acetaminophen is also not within the scope of practice for NAPs, as medication administration must be conducted by licensed nursing personnel or qualified healthcare professionals.