
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 $f(x)=\sin (\omega x+\varphi)$ ($\omega > 0$), $f'(x)$ is the derivative of $f(x)$. If $f(t)=0$, $f'(t) > 0$, and $f(x)$ does not have a minimum value in the interval $[t,t+1)$, determine the range of $\omega$.

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