
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 points $M(x_{1},0)$ and $N(x_{2}, \frac{\sqrt{2}}{2}A)$ are on the graph of the function $f(x)=A\sin (\omega x+\varphi)$ ($A > 0,\omega > 0$), and the minimum value of $|x_{1}-x_{2}|$ is $\frac{\pi}{3}$, calculate the value of $\omega$.

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