
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 $F_{1}$ and $F_{2}$ be the left and right foci of the ellipse $E$: $\frac{x^{2}}{13} + \frac{y^{2}}{4} = 1$, and $P$ be any point on the ellipse (point $P$ does not coincide with the left and right vertices). Calculate the maximum area of $\triangle F_{2}PF_{1}$.

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