
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 $\triangle ABC$, the angles opposite sides $a$, $b$, and $c$ are $A$, $B$, and $C$ respectively, and satisfy $a^{3}-b^{2}c=ab^{2}-c^{3}$.  
$(1)$ Find the measure of angle $B$;  
$(2)$ If the area of $\triangle ABC$ is $\frac{\sqrt{3}}{6}$ and $b=4$, find the perimeter of $\triangle ABC$.  
Reference formula: $m^{3}+n^{3}=\left(m+n\right)(m^{2}-mn+n^{2})$

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