
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]


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In the parallelogram \(ABCD\), the longer side \(AD\) is 5. The angle bisectors of angles \(A\) and \(B\) intersect at point \(M\).

Find the area of the parallelogram, given that \(BM = 2\) and \(\cos \angle BAM = \frac{4}{5}\).

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