
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]

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# Your action step 3

...

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system

The side \( AB \) of parallelogram \( ABCD \) is equal to \( 2 \), \( \angle A = 45^\circ \). Points \( E \) and \( F \) are located on the diagonal \( BD \), such that

\[ \angle AEB = \angle CFD = 90^\circ, \quad BF = \frac{3}{2} BE. \]

Find the area of the parallelogram.

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