
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
Given a large equilateral triangle with a side length of 4 units, there exists a smaller equilateral triangle such that its area is one-third the area of the larger triangle. If these two triangles represent bases of a trapezoid, find the length of the median of this trapezoid.
A) \( \frac{4\sqrt{3} + 4}{2} \) units
B) \( \frac{8 + 2\sqrt{3}}{3} \) units
C) \( \frac{2(\sqrt{3} + 1)}{\sqrt{3}} \) units
D) \( \frac{2\sqrt{2} + 2}{\sqrt{3}} \) units

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