
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 with their vertices on each vertex of a square of side length $2$. The sum of the areas of the four isosceles triangles is half the area of the square. What is the length of one of the two congruent sides of one of the isosceles triangles?
A) $\frac{\sqrt{5}}{2}$
B) $\frac{\sqrt{3}}{2}$
C) $\frac{\sqrt{2}}{2}$
D) $1$
E) $\frac{1}{2}$

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