
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
Triangle $ABC$ is isosceles with $AB = AC$. Let the bisectors of the exterior angles at $B$ and $C$ of triangle $ABC$ meet at point $D$. Calculate $\angle BDC$.
A) $\frac{1}{2}(90-A)$
B) $90-A$
C) $\frac{1}{2}(180-A)$
D) $180-A$
E) $180-2A$

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