Final answer:
The nurse should prioritize reporting the finding of productive cough with green sputum to the provider as it may indicate a bacterial infection in the respiratory system.
Step-by-step explanation:
The nurse should prioritize reporting the finding of productive cough with green sputum to the provider. This is because green sputum may indicate the presence of a bacterial infection in the respiratory system, such as pneumonia. The color change suggests the presence of inflammatory cells, such as white blood cells, which are commonly seen in infections.