
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 $f(x)=\sin (2x+ \frac {π}{3})+ \frac { \sqrt {3}}{3}\sin ^{2}x- \frac { \sqrt {3}}{3}\cos ^{2}x.$
(I) Find the smallest positive period of $f(x)$ and the equation of the symmetry axis of its graph;
(II) Translate the graph of the function $f(x)$ to the right by $\frac {π}{3}$ units to obtain the graph of the function $g(x)$, and find the range of $g(x)$ on the interval $[- \frac {π}{6}, \frac {π}{3}]$.

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