A 55-year-old male has been coughing for a week with several symptoms. What should you first administer?

Administering oxygen by non-rebreather mask is appropriate in this scenario because the symptoms associated with a week-long cough can indicate potential respiratory distress or significant hypoxia. A non-rebreather mask delivers concentrated oxygen to the patient, which is crucial for those presenting with respiratory issues where oxygen saturation levels might be compromised.

The non-rebreather mask provides a higher oxygen flow compared to other methods, allowing for a quick and effective increase in the oxygen content in the patient's bloodstream. This is especially critical if the patient exhibits difficulty breathing or signs of low oxygen saturation. By ensuring that the patient receives adequate oxygen, you can help address immediate threats to their respiratory function.

Other options like oxygen by nasal cannula, acetaminophen, or aspirin would not provide the same level of immediate support for potential hypoxemia. The nasal cannula, while useful for delivering lower concentrations of oxygen, does not match the urgency required in this scenario. Acetaminophen and aspirin serve purposes for pain or anti-inflammatory effects but do not address any immediate respiratory concerns the patient may be experiencing. Thus, starting with oxygen via non-rebreather mask is the best course of action to stabilize the patient's condition.