
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 in acute triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Let $\overrightarrow{m}=(\sqrt{3}, \sin A)$ and $\overrightarrow{n}=(\cos A, -1)$, and $\overrightarrow{m}$ is perpendicular to $\overrightarrow{n}$. Choose one of the following conditions to supplement the problem and solve it:
1. $\frac{\sin A + \sin C}{a+c} + \frac{\sin(2A+2C)}{4\cos B} = 0$;
2. $\frac{\sin A - \sin B}{\sin C} = \frac{c-2}{a+b}$.

Find:
1. The value of angle $A$;
2. If ____, find the range of the area of triangle $\triangle ABC$.

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