
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
If an arc of \( 60^\circ \) on circle \( A \) is the same length as an arc of \( 40^\circ \) on circle \( B \), and an arc of \( 30^\circ \) on circle \( B \) is as long as an arc of \( 90^\circ \) on circle \( C \), find the ratio of the area of circle \( A \) to the area of circle \( C \).

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