
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 $ABC$, the sides $a$, $b$, $c$ are opposite to angles $A$, $B$, $C$ respectively. It is known that $c= \sqrt{6}$ and $C= \frac{2\pi}{3}$.  
(Ⅰ) If $a= \sqrt{2}$, find $b$;  
(Ⅱ) 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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