
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 ellipse $\frac{x^{2}}{49}+ \frac{y^{2}}{24}=1$, if the angle between the lines connecting a point $P$ on the ellipse and the two foci $F\_1$ and $F\_2$ is a right angle, then $|PF\_1| \cdot |PF\_2| =$ _____ .

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