
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 sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, $c$, and $\sqrt{2}\cos C(a\cos B+b\cos A)+c=0$.

(I) Find the measure of angle $C$.

(II) If $a=\sqrt{2}$, $b=2$, find:

(i) The length of side $c$.

(ii) The value of $\sin(2B-C)$.

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