
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 $f(x)= \sqrt {3}\sin ωx+\cos (ωx+ \frac {π}{3})+\cos (ωx- \frac {π}{3})-1(ω > 0,x∈R)$, and the smallest positive period of the function $f(x)$ is $π$.
(I) Find the expression of the function $f(x)$;
(II) Translate the graph of the function $f(x)$ to the right by $\frac {π}{6}$ units to obtain the graph of the function $y=g(x)$, and find the range of the function $y=g(x)$ on $[0, \frac {π}{2}]$.

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