
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 the function $f(x)=2\sqrt{3}\sin \frac{x}{3}\cos \frac{x}{3}-2\sin^{2} \frac{x}{3}$.

(I) Find the range of the function $f(x)$ if $x\in [0,\pi ]$.

(II) In $\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $f(C)=1$ and ${{b}^{2}}=ac$, find the value of $\sin A$.

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