
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 six points \( P, Q, R, S, T, \) and \( U \) equally spaced around a circle of radius \( 2 \) cm. The inner circle has a radius of \( 1 \) cm. The shaded region has three lines of symmetry. Which of the following gives the area, in \( \text{cm}^2 \), of the shaded region?
A) \( 2\pi + 3 \)  
B) \( 3\pi + 2 \)  
C) \( \frac{4\pi + 3}{2} \)  
D) \( 3(\pi + 2) \)  
E) \( 4\pi + 3 \)  

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