
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the hyperbola $C$: $\dfrac{x^{2}}{9} - \dfrac{y^{2}}{16} = 1$, with its left and right foci being $F_{1}$ and $F_{2}$ respectively, and $P$ is a point on the right branch of $C$, and $|PF_{2}| = \dfrac{8}{15}|F_{1}F_{2}|$, then the area of $\triangle PF_{1}F_{2}$ is $\boxed{\text{A: } \dfrac{80}{3}}$.

Present the answer in LaTex format: \boxed{Your answer}
user