
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 $f\left(x\right)=\sin \left(3x+\varphi \right)(|\varphi | \lt \frac{π}{2}$) is an odd function, if for any $\alpha \in [-\frac{π}{9}$,$\frac{2π}{9}]$, there exists $\beta \in [-\frac{π}{9}$,$\alpha ]$, such that $f\left(\alpha \right)+f\left(\beta \right)=0$, then the range of real number $\alpha$ is ______.

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