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