
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 $f(x)=4\cos (ωx- \frac {π}{6})\sin (π-ωx)-\sin (2ωx- \frac {π}{2})$, where $ω > 0$.
(1) Find the range of the function $f(x)$.
(2) If $y=f(x)$ is an increasing function in the interval $[- \frac {3π}{2}, \frac {π}{2}]$, find the maximum value of $ω$.

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