Final answer:
The nurse should prioritize addressing the physiological needs first, as indicated by Maslow's hierarchy of needs, due to the patient showing signs of respiratory distress and elevated heart rate.
Step-by-step explanation:
According to Maslow's hierarchy of needs, the nurse should address physiological needs first. These needs are the most critical for survival, which includes the need for oxygen, which is evident in the patient's increased respirations and cyanosis.
The patient's elevated pulse rate is another sign of physiological distress. In this situation, physiological needs take precedence over other levels such as self-esteem, love and belonging, and self-actualization, as outlined by Maslow. Immediate medical attention is required to manage the symptoms and prevent further health deterioration.