
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 $f(x)=\sin (\omega x+\varphi)$ ($\omega > 0$), if there exists a real number $x_{0}$, such that for any real number $x$, the inequality $f(x_{0})\leqslant f(x)\leqslant f(x_{0}+2016\pi)$ holds, then the minimum value of $\omega$ is \_\_\_\_\_\_.

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