
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 $\vartriangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, given that $c=2$, $C=\dfrac{\pi }{3}$.

(1) If the area of $\vartriangle ABC$ is equal to $\sqrt{3}$, find $a$ and $b$;

(2) If $\sin B=2\sin A$, find the area of $\vartriangle ABC$.

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