
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. The vectors $\overrightarrow{m} = (-1, 1)$ and $\overrightarrow{n} = (\cos B \cos C, \sin B \sin C - \frac{\sqrt{3}}{2})$, and it is given that $\overrightarrow{m} \perp \overrightarrow{n}$.

(1) Find the magnitude of angle $A$.

(2) Given the following three conditions: ① $a=1$; ② $2c-(\sqrt{3}+1)b=0$; ③ $B=45°$, choose two more conditions to determine triangle $ABC$ and calculate the area of the determined triangle $ABC$.

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