
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
$a$,$b$,$c$ are the opposite sides of angles $A$,$B$,$C$ in $\triangle ABC$, given $a\sin \left(A-B\right)=\left(c-b\right)\sin A$.<br/>$(1)$ Find $A$;<br/>$(2)$ If point $D$ lies on segment $BC$, $∠ADC=\frac{π}{3}$, $AD=3$, and the area of $\triangle ABC$ is $3\sqrt{3}$, find the perimeter of $\triangle ABC$.

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