
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 \( a \) and \( b \) be two positive numbers, and \( a > b \). Points \( P \) and \( Q \) are on the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\). The line connecting point \( A(-a, 0) \) and \( Q \) is parallel to the line \( OP \) and intersects the \( y \)-axis at point \( R \). If \( O \) is the origin, find the value of \(\frac{|AQ| \cdot |AR|}{|OP|^2}\).

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