
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
In $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively, and $\sin A=2\sin B$,

(1) If $C= \frac {3\pi}{4}$, and the area of $\triangle ABC$ is $\frac {9 \sqrt {2}}{4}$, find the value of $a$;

(2) Find the value of $\frac {\sin (C-A)}{\sin B}-8\sin ^{2} \frac {C}{2}$.

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