
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, nonvertical lines in the $xy$-coordinate plane intersect to form a $30^{\circ}$ angle. One line has a slope equal to $3$ times the slope of the other line. What is the greatest possible value of the product of the slopes of these two lines?
A) 0.5  
B) \(\frac{2}{3}\)  
C) 1  
D) 2

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