
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
The graph of the function $f\left(x\right)=\sin (x-\frac{π}{6})$ is shifted to the right by $\frac{π}{6}$ units, and then all the x-coordinates of the points are halved while the y-coordinates remain unchanged. This results in the graph of a function $g\left(x\right)$. The solution set of the inequality $g\left(x\right)-g(\frac{2023π}{2}) \gt 0$ in the interval $\left[0,\pi \right]$ is ____.

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