
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 $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively. Given vectors $\overrightarrow {m}=(\cos A，\sin A)$ and $\overrightarrow {n}=( \sqrt {2}-\sin A，\cos A)$, and $| \overrightarrow {m}+ \overrightarrow {n}|=2$.
(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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