
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
Given triangle $\triangle ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, and vectors $\overrightarrow{p}=(a,c-b)$, $\overrightarrow{q}=(\sin C+\sin B,\sin A+\sin B)$, where $\overrightarrow{p} \parallel \overrightarrow{q}$. <br/>$(1)$ Find angle $C$; <br/>$(2)$ If $c=3\sqrt{2}$ and the area of $\triangle ABC$ is $\frac{3\sqrt{3}}{2}$, find the perimeter of $\triangle ABC$.

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