
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 $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and it is given that $3(b^{2}+c^{2})=3a^{2}+2bc$.
1. If $a=2$, $b+c=2 \sqrt {2}$, find the area $S$ of $\triangle ABC$.
2. If $\sin B= \sqrt {2}\cos C$, find the value of $\cos C$.

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