
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. Inside it, three congruent isosceles triangles are constructed such that their bases collectively cover the entire perimeter of the equilateral triangle equally. The sum of the areas of these three isosceles triangles equals the area of the equilateral triangle. Find the length of one of the congruent sides of one of the isosceles triangles.

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