
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 graph of the function $f(x)=A\sin(\omega x+\varphi)$ (where $A > 0, \omega > 0)$ intersects the line $y=m$ at three consecutive points with the x-coordinates $\frac{\pi}{6}$, $\frac{\pi}{3}$, and $\frac{2\pi}{3}$, find the value of the real number $\omega$.

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