
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
Consider square \(ABCD\) with a side length of 10 units. Inside it, there is a smaller square \(PQRS\), rotated 45 degrees with respect to \(ABCD\), such that each side of \(PQRS\) can be extended to pass through a vertex of \(ABCD\). Given that the distance from vertex \(A\) to the nearest point \(P\) on square \(PQRS\) is 2 units, calculate the area of square \(PQRS\).
A) 100
B) 121
C) 144
D) 169

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