
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 $f(x)= \frac{1-\cos 2ωx}{2}+ \sqrt{3}\sin ωx\cos ωx$, the smallest positive period of the function $f(x)$ is $π$, and $ω > 0$.
(1) Find the analytic expression of the function;
(2) When $x\in\[- \frac{π}{12}, \frac{π}{2}\]$, find the range of the function.

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