
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 units. Right-angled isosceles triangles are constructed with their bases on each side of the equilateral triangle. The total area of these three right-angled isosceles triangles is equal to the area of the equilateral triangle. Find the length of the congruent sides of one of the right-angled isosceles triangles.
A) $\frac{\sqrt{3}}{2}$
B) $\frac{\sqrt{2}}{2}$
C) $\frac{\sqrt{6}}{3}$
D) $\frac{\sqrt{6\sqrt{3}}}{3}$
E) $\sqrt{3}$

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