
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
In a geometric setting, a large equilateral triangle and a smaller equilateral triangle are such that the area of the smaller triangle is one-third the area of the larger triangle. The side length of the large equilateral triangle is 3 units. A trapezoid is formed using the sides of these triangles as the lengths of the parallel bases. Calculate the length of the median of this trapezoid.
A) \( \frac{3\sqrt{3}}{2} \)
B) \( \frac{3+\sqrt{3}}{2} \)
C) \( 2\sqrt{3} \)
D) \( \frac{4 + \sqrt{3}}{2} \)

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