
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 $f(x)=2 \sqrt {3}\tan ( \frac {x}{2}+ \frac {π}{4})\cos ^{2}( \frac {x}{2}+ \frac {π}{4})-\sin (x+π)$.
(I) Find the domain and the minimum positive period of $f(x)$;
(II) If the graph of $f(x)$ is shifted to the right by $\frac {π}{6}$ units to obtain the graph of function $g(x)$, find the maximum and minimum values of function $g(x)$ on the interval $[0,π]$.

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