
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 right triangle $ABC$ where angle $C$ is $90^\circ$, the bisectors of the exterior angles at $B$ and $C$ meet at point $D$. Calculate angle $BDC$.
A) $\frac{A}{2}$ 
B) $A$ 
C) $90^\circ - A$ 
D) $\frac{180^\circ - A}{2}$

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