
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 an isosceles triangle with $\angle ABC = \angle ACB$ and $AB = AC = 2$. Determine the length of $BD$, where $D$ is the point on $BC$ such that $AD$ is the angle bisector of $\angle BAC$.
A) 1
B) 2
C) $\sqrt{2}$
D) $\sqrt{3}$
E) $\frac{\sqrt{5} - 1}{2}$

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