
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 a circle, triangle $ABC$ is inscribed such that $\angle ABC = \angle ACB$. $AD$ and $CD$ are tangents from a point $D$ outside the circle. If $\angle ABC = 3 \angle D$, $\angle ADA$ is an external angle at $D$ formed as $AD$ intersects the circle at another point $A_D$, and $\angle BAC = \alpha$, express $\alpha$ in terms of $\pi$.

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