
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 $f\left(x\right)=2\sin \omega x\left(\omega\ \ \gt 0\right)$, if there are exactly two distinct real numbers $a$ and $b$ in the interval $[0,\frac{π}{2}]$ such that $f\left(a\right)+f\left(b\right)=4$, then the range of real number $\omega$ is ______.

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