
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 has a side length of 4 units. Within this larger triangle, a smaller equilateral triangle is oriented such that its vertices coincide with those of the large triangle's base and its area is one-fourth that of the larger triangle. A trapezoid is formed by the sides of these two triangles. Calculate the median of the trapezoid.
A) $2 + \sqrt{2}$ units
B) 3 units
C) $2\sqrt{3}$ units
D) $\frac{6+\sqrt{2}}{2}$ units

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