
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
The internal angles $A$, $B$, $C$ of triangle $ABC$ are opposite to sides $a$, $b$, $c$, respectively. It is known that the area of $\triangle ABC$ is $\dfrac{{a}^{2}}{3\sin A}$.

$(1)$ Find $\sin B\sin C$;

$(2)$ If $6\cos B\cos C=1$ and $a=3$, find the perimeter of $\triangle ABC$.

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