
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
Points \(P, Q, R,\) and \(S\) lie in the plane of the square \(EFGH\) such that \(EPF\), \(FQG\), \(GRH\), and \(HSE\) are equilateral triangles. If \(EFGH\) has an area of 25, find the area of quadrilateral \(PQRS\). Express your answer in simplest radical form.

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