
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
Choose one of the following conditions from (1) $a\sin \left(B+C\right)+c\sin C-b\sin B=2a\sin C\sin B$, (2) $\frac{cosB}{cosC}+\frac{b}{c-\sqrt{2}a}=0$, (3) $2a^{2}=(a^{2}+b^{2}-c^{2})(1+\tan C)$, and fill in the blank in the question below, and answer the corresponding questions.  
Given $\triangle ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, and satisfying ____.  
$(1)$ Find the measure of angle $B$;  
$(2)$ If the area of $\triangle ABC$ is $3$ and $a=2\sqrt{2}$, find the value of $\sin A\sin C$.

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