
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
Two circles \( \mathcal{C}_{1} \) and \( \mathcal{C}_{2} \) intersect at the point \( (6,8) \), and the product of their radii is \( 45 \). Both circles are tangent to the x-axis and to the line \( y = nx \) where \( n > 0 \). Find the value of \( n \).

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