
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, which divides it into segments \(BE = 2\) and \(EC = 3\). The circumcircle of triangle \(ABE\) intersects the diagonal \(BD\) at a second point \(G\). Find the area of triangle \(AGE\).

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