
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
If the function $f(x)=\sin(\omega x+\frac{\pi}{6})$ ($\omega>0$) has a distance of $\frac{\pi}{2}$ between two adjacent axes of symmetry on its graph, and the graph of the function is centrally symmetric about the point $(x_{0}, 0)$ where $x_{0} > 0$, then the minimum value of $x_{0}$ is ______.

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