
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 bisector of angle \(A\) intersects side \(BC\) at point \(M\), and the bisector of angle \(C\) intersects side \(AD\) at point \(N\). The area of the quadrilateral formed by the intersection of the angle bisectors \(AM\) and \(CN\) with segments \(BN\) and \(DM\) is \(\frac{6}{5}\). Find the angles of the parallelogram \(ABCD\), given that \(AB = 3\) and \(AD = 5\).

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