
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 $\triangle ABC$, angles $A$, $B$, and $C$ are opposite to sides $a$, $b$, and $c$, respectively, and $3a = 2b$,
(I) If $B = 60^{\circ}$, find the value of $\sin C$;
(II) If $b - c = \frac{1}{3}a$, find the value of $\cos C$.

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