
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 $2$. At each side of this triangle, an isosceles triangle is constructed externally with the base on the equilateral triangle's side and such that the area of each isosceles triangle is one fourth the area of the equilateral triangle. What is the length of one of the two congruent sides of one of these isosceles triangles?
A) $\frac{\sqrt{7}}{3}$
B) $\frac{\sqrt{15}}{3}$
C) $\frac{\sqrt{19}}{4}$
D) $\frac{\sqrt{21}}{4}$
E) $\frac{2\sqrt{3}}{3}$

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