
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
Given that circles $C_{1}$ and $C_{2}$ intersect at two points, one of which has coordinates $(9,6)$, and the product of their radii is 68. If the $x$-axis and the line $y = mx$ (where \(m > 0\)) are both tangent to the two circles, find the value of $m$.

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