
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\frac {\sin A}{\sin B+\sin C}=1- \frac {a-b}{a-c}$.  
$(I)$ Let $\overrightarrow{m}=(\sin A,1)$, $\overrightarrow{n}=(8\cos B,\cos 2A)$, determine the shape of $\triangle ABC$ when $\overrightarrow{m}\cdot \overrightarrow{n}$ is maximized.  
$(II)$ If $b= \sqrt {3}$, find the range of the perimeter of $\triangle ABC$.

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