<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 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? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
25
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?
test