
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
On the side \(BC\) of the square \(ABCD\), a point \(E\) is chosen such that it divides the side into segments \(BE=2\) and \(EC=3\). The circumscribed circle of the triangle \(ABE\) intersects the diagonal \(BD\) for the second time at point \(G\). Find the area of the triangle \(AGE\).

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