
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 $f\left(x\right)=\sin ^{2}\frac{ωx}{2}+\frac{1}{2}\sin \omega x-\frac{1}{2}(\omega\ \ \gt 0,x\in R)$, if $f\left(x\right)$ has no zero points in the interval $\left(\pi ,2\pi \right)$, the range of $\omega$ is ____.

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