
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
A series of five concentric circles are drawn with radii of 2, 4, 6, 8, and 10. Starting from the innermost circle which is painted black, the next ring is white, followed by a black ring, then white, and the outermost ring is painted black. Calculate the ratio of the black area to the white area. Express your answer as a common fraction.

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