
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 sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $\frac{c}{{b-a}}=\frac{{\sin A+\sin B}}{{\sin A+\sin C}}$.  
$(Ⅰ)$ Find the measure of angle $B$.  
$(Ⅱ)$ If $\sin C=2\sin A$ and $S_{\triangle ABC}=2\sqrt{3}$, find $a$ and $c$.  
$(Ⅲ)$ If $b=\sqrt{3}$, $ac=1$, find the perimeter of $\triangle ABC$.

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