
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
The circle has radius \(1 \mathrm{~cm}\). Two vertices of the square lie on the circle. One edge of the square goes through the center of the circle. What is the area of the square?
A) \(\frac{4}{5} \mathrm{~cm}^{2}\)
B) \(\frac{\pi}{5} \mathrm{~cm}^{2}\)
C) \(1 \mathrm{~cm}^{2}\)
D) \(\frac{\pi}{4} \mathrm{~cm}^{2}\)
E) \(\frac{5}{4} \mathrm{~cm}^{2}\)

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