
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
In a parallelogram with sides \(a\) and \(b\), and an angle \(\alpha\) between these sides, the bisectors of its four angles are drawn. Find the area of the quadrilateral formed by the intersection points of these bisectors.

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