
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 $f(x)=\sin^{2}\frac{\omega x}{2}+\frac{1}{2}\sin\omega x+\frac{1}{2}$, where $\omega \in \mathbb{R}$ and $x \in \mathbb{R}$. If $f(x)$ has no zeros in the interval $(0,\pi)$, determine the range of values for $\omega$.

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