
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 $x^{2}- \frac{y^{2}}{24}=1$, let the focal points be F<sub>1</sub> and F<sub>2</sub>, respectively. If P is a point on the left branch of the hyperbola such that $|PF_{1}|=\frac{3}{5}|F_{1}F_{2}|$, find the area of triangle $\triangle PF_{1}F_{2}$.

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