
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 $\triangle ABC$, $D$ is a point on $BC$, $AD$ bisects $\angle BAC$, and $BD=2DC$. Find:<br/>
$(1)$ The value of $\frac{\sin B}{\sin C}$;<br/>
$(2)$ If $\angle BAC=60^{\circ}$ and $AD=1$, find the length of $AB$.

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