
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
A pair of lines, \( L_1 \) and \( L_2 \), have equations \( y = mx \) and \( y = nx \) respectively. \( L_1 \) makes three times the angle with the positive x-axis that \( L_2 \) does, and the slope of \( L_1 \) is 9 times the slope of \( L_2 \). Assuming neither line is horizontal, determine the value of \( mn \).
A) \(\frac{81}{13}\)  
B) \(\frac{27}{13}\)  
C) \(\frac{12}{13}\)  
D) \(3\)

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