
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 moving point on the major axis of the ellipse \(\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1\). A line with slope \( k \) passes through \( P \) and intersects the ellipse at points \( A \) and \( B \). If the value of \( |PA|^{2} + |PB|^{2} \) depends only on \( k \) and not on the position of \( P \), find the value of \( k \).

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