
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 \( P \) be a point on the ellipse \(\frac{x^{2}}{100} + \frac{y^{2}}{36} = 1\), and let \( F_{1} \) and \( F_{2} \) be the foci. If the area of the triangle \(\triangle P F_{1} F_{2}\) is 36, then \(\angle F_{1} P F_{2} =\) ____ .

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