
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 angles $A$, $B$, $C$ correspond to the sides $a$, $b$, $c$, respectively. The vectors $\overrightarrow{m}=(\sin B, 5\sin A + 5\sin C)$ and $\overrightarrow{n}=(5\sin B - 6\sin C, \sin C - \sin A)$ are perpendicular.

(1) Find the value of $\sin A$;

(2) If $a = 2\sqrt{2}$, find the maximum value of the area $S$ of triangle $ABC$.

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