
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 opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively. It is given that $\overrightarrow{a}=(\sin B-\sin C,\sin C-\sin A)$, $\overrightarrow{b}=(\sin B+\sin C,\sin A)$, and $\overrightarrow{a}\perp \overrightarrow{b}$.

$(1)$ Find the magnitude of angle $B$;  
$(2)$ If the radius of the circumcircle of $\triangle ABC$ is $1$, find the area of $\triangle ABC$.

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