
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
Three concentric circles have radii 4, 3, and 2 respectively. Two distinct lines pass through the center, creating shaded and unshaded regions. The area of the shaded regions is $\frac{3}{4}$ of the unshaded regions. Determine the radian measure of the acute angle formed by the two lines.
A) $\frac{\pi}{4}$  
B) $\frac{12\pi}{77}$  
C) $\frac{6\pi}{77}$  
D) $\frac{\pi}{10}$  
E) $\frac{\pi}{7}$

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