
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
In the Cartesian coordinate plane, circles \( C_{1} \) and \( C_{2} \) intersect at points \( P \) and \( Q \). The coordinates of point \( P \) are \( (3, 2) \), and the product of the radii of the two circles is \( \frac{13}{2} \). If both circles are tangent to the line \( l: y = kx \) and the x-axis, find the equation of the line \( l \).

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