
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

Through the vertex \( A \) of an equilateral triangle \( A B C \), a line is drawn at an angle \( \alpha \left(0<\alpha<\frac{\pi}{3}\right) \) to \( A C \), intersecting \( B C \) at point \( D \). Find the ratio of the area of triangle \( A D C \) to the area of triangle \( A B C \).

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