**Core Concept**
The patient's history of chronic sputum production and previous pneumothorax suggests a diagnosis of cystic fibrosis (CF), a genetic disorder characterized by abnormal chloride ion transport in the lungs, leading to thickened mucus and recurrent respiratory infections. The patient's symptoms and CXR findings are consistent with a complication of CF, likely bronchiectasis or a pulmonary abscess.

**Why the Correct Answer is Right**
The patient's chronic sputum production and recurrent respiratory infections indicate a high risk of Pseudomonas aeruginosa infection, a common pathogen in CF patients. Anti-pseudomonas antibiotic regimen is the most appropriate treatment option as it targets the likely causative pathogen. The use of broad-spectrum antibiotics (Option B) may not be effective against Pseudomonas, and increasing bronchodilator therapy (Option A) may not address the underlying infection. Oral steroids (Option D) may be used to reduce inflammation, but they are not the most helpful treatment option in this scenario.

**Why Each Wrong Option is Incorrect**
**Option A:** Increasing bronchodilator therapy may provide temporary relief from bronchospasm but does not address the underlying infection.
**Option B:** Broad-spectrum antibiotic therapy may not be effective against Pseudomonas aeruginosa, which is often resistant to multiple antibiotics.
**Option D:** Oral steroids may be used to reduce inflammation in CF patients, but they are not the most effective treatment option in this scenario.

**Clinical Pearl / High-Yield Fact**
Cystic fibrosis patients are at high risk of developing Pseudomonas aeruginosa infections, which can be challenging to treat. A high index of suspicion and prompt initiation of anti-pseudomonas antibiotic regimen are essential in managing these patients.

**✓ Correct Answer:** C. **Initiate anti-pseudomonas antibiotic regimen**