Final answer:
The nurse should first initiate airborne precautions because the patient's symptoms are indicative of potential airborne infections. Obtaining a sputum sample, administering antipyretics, and securing venous access are important actions to take for the patient's overall care, but they should be done after airborne precautions.
Step-by-step explanation:
The nurse should first initiate airborne precautions because the patient's symptoms, including a productive cough and night sweats, are indicative of potential airborne infections.
Initiating airborne precautions would involve placing the patient in a negative pressure room with appropriate personal protective equipment, such as an N95 respirator mask.
Obtaining a sputum sample, administering antipyretics, and securing venous access are important actions to take for the patient's overall care, but they should be done after airborne precautions to prevent the potential spread of airborne pathogens.