
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $b\sin A=(3b-c)\sin B$
(1) If $2\sin A=3\sin B$, and the perimeter of $\triangle ABC$ is $8$, find $c$
(2) If $\triangle ABC$ is an isosceles triangle, find $\cos 2B$.

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