
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 a square \(PQRS\) with side length \(s\), points \(T\) and \(U\) are taken respectively on sides \(PQ\) and \(PS\) such that \(PT = PU\). If \(QT = \frac{1}{3}PQ\) and \(US = \frac{1}{3}PS\), find the area of quadrilateral \(RUTS\).

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