
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 $L_1$ and $L_2$ are $y=3mx$ and $y=nx$, respectively. Suppose $L_1$ makes three times as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does $L_2$, and that $L_1$ has 3 times the slope of $L_2$. If $L_1$ is not vertical, then find the product $mn$.

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