
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 that $a$, $b$, $c$ are respectively the sides opposite the angles $A$, $B$, $C$ of $\triangle ABC$, and that $\sin^2B=2\sin A\sin C$.
(Ⅰ) If $a=b$, find $\cos B$;
(Ⅱ) Assume $B=90^{\circ}$ and $a=\sqrt{2}$, find the area of $\triangle ABC$.

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