
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 square \(ABCD\), points \(P\) and \(Q\) are on \(\overline{AD}\) and \(\overline{AB}\), respectively. Segments \(\overline{BP}\) and \(\overline{CQ}\) intersect perpendicularly at \(R\), where \(BR = 3\) and \(PR = 4\). Find the area of the square.

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