
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 $\Delta ABC$, $a, b, c$ are the sides opposite to angles $A, B, C$ respectively, and $a^2 + c^2 - \sqrt{3}ac = b^2$, $3a = 2b$.

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

(II) If $b = 6$, find the area of $\Delta ABC$.

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