
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
An equilateral triangle with side length 4 units is inscribed in a square. Another smaller equilateral triangle, which has half the area of the larger triangle, is inscribed in a parallelogram. If one base of the trapezoid is the side of the larger triangle and the other base is the side of the smaller triangle, find the length of the median of the trapezoid.
A) \(2\)
B) \(2\sqrt{2}\)
C) \(2 + \sqrt{3}\)
D) \(2 + \sqrt{2}\)

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