
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 $f(x) = 2 \sqrt {3} \sin\left(\frac {x}{2}+ \frac {\pi}{4}\right)\cos\left(\frac {x}{2}+ \frac {\pi}{4}\right)-\sin(x+\pi)$:
(I) Find the smallest positive period of $f(x)$;
(II) If the graph of $f(x)$ is translated by the vector $\overrightarrow {a} = \left( \frac {\pi}{6}, 0\right)$ to obtain the graph of the function $g(x)$, determine the monotonic intervals and the range of $g(x)$ on the interval $[0, \pi]$.

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