
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
Given a triangle $\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively. It is known that $\cos C= \frac{ {\sqrt {3}}}{3}$, $a=3$, and $(b-a)(\sin B+\sin A)=(b-c)\sin C$.

(I) Find the value of $\sin B$;

(II) Find the area of $\triangle ABC$.

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