
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 $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given that $3b^{2}+3c^{2}-3a^{2}=4\sqrt{2}bc$.

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

(2) Find the value of $\frac{2\sin \left( A+\frac{\pi }{4} \right)\sin \left( B+C+\frac{\pi }{4} \right)}{1-\cos 2A}$.

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