
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. It is known that $c=2$ and $C=\frac{\pi}{3}$.

(1) If $a=\frac{2\sqrt{3}}{3}$, find $A$;
(2) If $\sin B=2\sin A$, find the area of $\triangle ABC$.

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