
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 such that \( a > b \). Points \( P \) and \( Q \) lie on the ellipse \(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\). If the line connecting point \( A(a, 0) \) and \( Q \) is parallel to the line \( OP \) and intersects the \( y \)-axis at point \( R \), where \( O \) is the origin, then \(\frac{|AQ| \cdot |AR|}{|OP|^2} =\)

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