
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 triangle $ABC$, $\overline{AB} = \overline{AC}$, and $B$ and $C$ lie on a circle centered at $O$. Lines $\overline{BA}$ and $\overline{BC}$ are tangents to the circle at $A$. $\angle BAC = 80^\circ$. The circle intersects $\overline{BO}$ at $D$. What is $\frac{BD}{BO}$?
A) $\sin(10\degree)$
B) $\sin(20\degree)$
C) $\sin(40\degree)$
D) $\sin(50\degree)$

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