
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
The ellipse \(\frac{x^{2}}{2002^{2}}+\frac{y^{2}}{1949^{2}}=1\) intersects with two lines passing through the origin at points \(A, B, C,\) and \(D\). The slope of line \(AB\) is \(k\), and the slope of line \(CD\) is \(-\frac{1949^{2}}{2002^{2} \cdot k}\). Given that there exists a triangle \(\triangle PQR\) such that \(PQ=OA\), \(PR=OC\), and \(\angle QPR=\left|\angle AOC-\frac{\pi}{2}\right|\), find \(QR-\qquad\).

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