
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 arrangement, a large equilateral triangle with side length 4 units and a smaller equilateral triangle whose area is one-third of the larger triangle are positioned to form a trapezoid. Find the median of this trapezoid whose bases are constituted by the sides of these two triangles.
A) $2\sqrt{3}$ units 
B) $2 + \sqrt{3}$ units 
C) $2 + \frac{2}{\sqrt{3}}$ units 
D) $2 + \frac{2\sqrt{3}}{3}$ units

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