
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 $f(x) = \sin(2x + \frac{\pi}{3}) + \frac{\sqrt{3}}{3}\sin 2x - \frac{\sqrt{3}}{3}\cos 2x$.
(I) Translate the graph of the function $f(x)$ to the right by $\frac{\pi}{3}$ units to obtain the graph of the function $g(x)$. Find the range of $g(x)$ on the interval $(-\frac{\pi}{6}, \frac{\pi}{3}]$.

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