
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 an arbitrary point on the ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) other than the endpoints of the major axis. \( F_{1} \) and \( F_{2} \) are its left and right foci respectively, and \( O \) is the center. Find the value of \( \left|P F_{1}\right| \cdot \left|P F_{2}\right| + |O P|^{2} \).

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