
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 an area \(S\), the bisectors of its interior angles are drawn. The area of the quadrilateral formed at their intersection is \(Q\). Find the ratio of the lengths of the sides of the parallelogram.

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