
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 $\triangle ABC$, let the sides opposite to angles $A$, $B$, $C$ be $a$, $b$, $c$ respectively. Given vectors $\overrightarrow{m}=(\cos A,\sin A)$ and $\overrightarrow{n}=( \sqrt {2}-\sin A,\cos A)$, and $\overrightarrow{m} \cdot \overrightarrow{n}=1$.

1. Find the measure of angle $A$.
2. If $b=4 \sqrt {2}$ and $c= \sqrt {2}a$, find the area of $\triangle ABC$.

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