
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
A square  $ABCD$  with side length  $1$  is inscribed in a circle. A smaller square lies in the circle with two vertices lying on segment  $AB$  and the other two vertices lying on minor arc  $AB$ . Compute the area of the smaller square.


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