
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

The side \(AB\) of parallelogram \(ABCD\) equals 2, and \(\angle A = 45^\circ\). Points \(E\) and \(F\) are located on the diagonal \(BD\), with the following conditions:

\(\angle AEB = \angle CFD = 90^\circ\) and \(BF = \frac{3}{2} BE\).

Find the area of the parallelogram.

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