
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 nonhorizontal, non vertical lines in the $xy$-coordinate plane intersect to form a $30^{\circ}$ angle. One line has slope equal to $3$ times the slope of the other line. What is the greatest possible value of the product of the slopes of the two lines?
A) $\frac{1}{\sqrt{3}}$
B) $\frac{1}{3}$
C) $\sqrt{3}$
D) $1$
E) $2$

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