
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 $f(x)=\sin \left( {\omega x+\frac{\pi }{6} } \right)(\omega > 0)$, the distance between two adjacent symmetry axes of the function's graph is $\frac{\pi }{2}$, and the graph is symmetrical about the point $(x_{0},0)$, where $x_{0} \in \left[ 0,\frac{\pi }{2} \right]$. Find the value of $x_{0}$.

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