
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 \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \) that is not an endpoint of the major axis. Let \( F_1 \) and \( F_2 \) be the left and right foci of the ellipse, respectively, and \( O \) be the center. Then, \(\left|PF_1\right| \cdot \left|PF_2\right| + \left|OP\right|^2\) equals what value?

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