
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
Let $P$ be a point on the upper branch of the hyperbola $\frac{x^{2}}{a^{2}}-y^{2}=1 (a > 0)$, and $\angle F_{1}PF_{2}=\frac{2π}{3}$ ($F_{1}$ and $F_{2}$ are the left and right foci, respectively). Calculate the area of $\triangle F_{1}PF_{2}$.

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