
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
Given the area of $\triangle ABC$ is $\frac{1}{2}$, $AB=1$, $BC= \sqrt{2}$.

(1) Find the length of $AC$;  
(2) Let $f(x)=\cos^{2}x+2 \sqrt{3}\sin x\cos x-\sin^{2}x$, if $f(B)=- \sqrt{3}$, find $\sin A$.

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