
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 the quadrilateral $ABCD$ in the plane, where $AB=6$, $\angle ADC=90^{\circ}$, $\angle A=60^{\circ}$, $\cos \angle ABD=-\frac{1}{7}$, and the area of $\triangle BCD$ is $39\sqrt{3}$.  
$(1)$ Find the value of $\sin \angle ADB$.  
$(2)$ Find the length of the side $BC$.

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