
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
The left and right foci of the ellipse $\dfrac{x^{2}}{4} + \dfrac{y^{2}}{2} = 1$ are denoted as $F_{1}$ and $F_{2}$, respectively. A point $P$ on the ellipse satisfies $|PF_{1}| - |PF_{2}| = 2$. The area of $\triangle PF_{1}F_{2}$ is __________.

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