
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
In triangle \(ABC\), the radii of the circumscribed and inscribed circles are given as \(R\) and \(r\) respectively. Let \(A_1, B_1, C_1\) be the points where the angle bisectors of triangle \(ABC\) intersect the circumscribed circle. Find the ratio of the areas of triangles \(ABC\) and \(A_1B_1C_1\).

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