
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 the internal angles $A$, $B$, $C$ of $\triangle ABC$ are respectively $a$, $b$, $c$. Given that $b\sin C+c\sin B=4a\sin B\sin C$ and $b^2+c^2-a^2=8$, the area of $\triangle ABC$ is \_\_\_\_\_.

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