
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 line passing through the origin intersects both the line $x = 1$ and the line $y = 1 + \frac{1}{\sqrt{3}}x$. The three lines create an equilateral triangle. What is the perimeter of the triangle?
A) $3 + 2\sqrt{3}$
B) $6$
C) $3 + 4\sqrt{3}$
D) $2\sqrt{6}$
E) $6 + \frac{\sqrt{3}}{3}$

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