
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
The equations of lines $L_1$ and $L_2$ are given by $y=mx$ and $y=nx$ respectively. $L_1$ makes three times the angle with the horizontal (measured counterclockwise from the positive x-axis) as does $L_2$, and $L_1$ has 3 times the slope of $L_2$. Find the product $mn$ if $L_1$ is not vertical.
A) 0  
B) 1  
C) 2  
D) -1

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