
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
As shown in the diagram, in the square \(ABCD\), \(AB = 2\). Draw an arc with center \(C\) and radius equal to \(CD\), and another arc with center \(B\) and radius equal to \(BA\). The two arcs intersect at \(E\). What is the area of the sector \(BAE\)?

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