
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 a triangle $\triangle ABC$ with the lengths of the sides opposite angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively. Let vector $\overrightarrow{m} = (a-c, a-b)$ and vector $\overrightarrow{n} = (a+b, c)$, and $\overrightarrow{m}$ is parallel to $\overrightarrow{n}$,  
(1) Find $B$;  
(2) If $a=1$ and $b= \sqrt{7}$, find the area of $\triangle ABC$.

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