
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 parallelogram \(ABCD\), the acute angle \(BAD\) is equal to \(\alpha\). Let \(O_{1}, O_{2}, O_{3}, O_{4}\) be the centers of the circles circumscribed around triangles \(DAB, DAC, DBC, ABC\), respectively. Find the ratio of the area of quadrilateral \(O_{1}O_{2}O_{3}O_{4}\) to the area of parallelogram \(ABCD\).

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