
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 $f(x)=\sin(2\omega x+\frac{2\pi}{3})-\frac{\sqrt{3}}{2}$, where $x\in[0,\frac{\pi}{2}]$ and $\omega\gt 0$, has exactly two zeros. Find the range of real number $\omega$.

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