**Core Concept**
The presence of a submandibular mass with a variety of bacteria, including branched, Gram-positive rods, suggests a diagnosis of actinomycosis, a chronic bacterial infection caused by Actinomyces species. This condition is characterized by the formation of abscesses and the presence of "sulfur granules," which are actually colonies of Actinomyces.

**Why the Correct Answer is Right**
Actinomyces species are anaerobic, Gram-positive bacteria that thrive in the oral cavity and gut. They can invade tissues and cause a range of symptoms, including pain, swelling, and abscesses. In the case of a submandibular mass, actinomycosis should be suspected, and the most clinically appropriate action is to obtain a biopsy for histopathological examination to confirm the diagnosis. This will involve sending the tissue sample to the laboratory for Gram stain, culture, and histopathological examination.

**Why Each Wrong Option is Incorrect**
**Option A:** Starting broad-spectrum antibiotics without a confirmed diagnosis may mask the symptoms and delay the diagnosis of actinomycosis, which requires specific treatment.

**Option B:** Incision and drainage of the abscess may provide temporary relief but will not address the underlying infection, which requires specific antibiotic therapy.

**Option C:** Fine-needle aspiration cytology (FNAC) may not provide sufficient tissue for diagnosis and may lead to a false-negative result.

**Clinical Pearl / High-Yield Fact**
Actinomyces species are typically found in the oral cavity and gut, and their infections often occur in individuals with a history of dental procedures, trauma, or immunosuppression.

**Correct Answer:** C. Biopsy for histopathological examination.