
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
Let $\triangle ABC$ have internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively. Given $\overrightarrow{m}=(\sin B,-2\sin A)$, $\overrightarrow{n}=(\sin B,\sin C)$ and $\overrightarrow{m}\perp \overrightarrow{n}$:

(Ⅰ) If $a=b$, find $\cos B$;

(Ⅱ) If $B=90^{\circ}$ and $a= \sqrt {2}$, find the area of $\triangle ABC$.

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