
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
Chords \( AB \) and \( AC \) are equal to each other. The inscribed angle formed by them in a circle is \( 30^{\circ} \). Find the ratio of the area of the part of the circle enclosed by this angle to the area of the entire circle.

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