
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 that the shortest distance from the center of symmetry to the axis of symmetry of the graph of the function $f(x)=\cos (2ωx- \frac {π}{3})-2\cos ^{2}ωx+2$ is $\frac {π}{4}$.
(1) Find the value of $ω$ and the equations of the center of symmetry and the axis of symmetry of the graph of the function $f(x)$.
(2) Find the range of the function $f(x)$ on the interval $[- \frac {π}{12}, \frac {π}{2}]$.

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