
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 function $g(x)$ is both a quadratic function and a power function, find the value of $f(-2023)+f(-2022)+\ldots +f(-1)+f(0)+f(1)\ldots +f(2022)+f(2023)$, where $f(x)=\frac{{x}^{3}}{g(x)+1}+1$.

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