
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 an ellipse $\frac{x^{2}}{49}+ \frac{y^{2}}{24}=1$ with a point $P$ on it such that the lines connecting $P$ to the ellipse's two foci $F\_1$ and $F\_2$ are perpendicular to each other.

(1) Calculate the eccentricity of the ellipse;

(2) Calculate the area of the triangle $PF\_1F\_2$.

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