
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 lengths of the sides opposite to $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$, respectively. Given $\overrightarrow{m}=(\sin C,\sin B\cos A)$ and $\overrightarrow{n}=(b,2c)$ with $\overrightarrow{m}\cdot \overrightarrow{n}=0$.

1. Find the measure of $\angle A$;
2. If $a=2 \sqrt {3}$ and $\sin B+\sin C=1$, find the area $S$ of $\triangle ABC$.

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