
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 that the average of sample data $x_{1}$, $x_{2}$, $\ldots$, $x_{2023}$ is $\overline{x}$, and the variance is $s^{2}$. If the average of the data $2(x_{1}+1)$, $2(x_{2}+1)$, $\ldots$, $2(x_{2023}+1)$ is $2(\overline{x}+1)$ and the variance is $4$ greater than the average, then the maximum value of $s^2-\overline{x}^2$ is ______.

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