
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.
1) If $a=\sqrt{3}$, $b=\sqrt{2}$, $B=45^{\circ}$, find angle $A$, $C$ and side $c$;
2) If $\frac{\cos B}{\cos C}=-\frac{b}{2a+c}$, $b=\sqrt{13}$, $a+c=4$, find the area of $\triangle ABC$.

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