
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
Four congruent isosceles triangles are constructed inside a square with each base lying along one side of the square. The apexes of all four isosceles triangles meet at the center of the square, dividing it into four congruent isosceles triangles. The side of the square is $2$ units. If the sum of the areas of the four isosceles triangles equals the area of the square, what is the length of the congruent sides of one of the isosceles triangles?
A) \( 1 \)
B) \( 2 \)
C) \( \dfrac{\sqrt{2}}{2} \)
D) \( \sqrt{2} \)
E) \( 2\sqrt{2} \)

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