
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
The diagram shows a square \(PQRS\) with edges of length 1, and four arcs, each of which is a quarter of a circle. Arc \(TRU\) has center \(P\); arc \(VPW\) has center \(R\); arc \(UV\) has center \(S\); and arc \(WT\) has center \(Q\). What is the length of the perimeter of the shaded region?

A) 6  
B) \((2 \sqrt{2} - 1) \pi\)  
C) \(\left(\sqrt{2} - \frac{1}{2}\right) \pi\)  
D) 2 \(\pi\)  
E) \((3 \sqrt{2} - 2) \pi\)

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