
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 distinct lines intersect at the center of three concentric circles with radii 4, 3, and 2. The area of the shaded regions formed by these lines is $\frac{5}{8}$ of the area of the unshaded regions. Determine the radian measure of the smallest angle formed by any two of these lines.
A) $\frac{\pi}{13}$
B) $\frac{3\pi}{13}$
C) $\frac{5\pi}{13}$
D) $\frac{8\pi}{13}$
E) $\frac{\pi}{6}$

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