
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 $x$ takes the values $-2023$, $-2022$, $-2021$, $\ldots$, $-2$, $-1$, $0$, $1$, $\frac{1}{2}$, $\frac{1}{3}$, $\ldots$, $\frac{1}{2021}$, $\frac{1}{2022}$, $\frac{1}{2023}$, calculate the value of the fraction $\frac{{x}^{2}-1}{{x}^{2}+1}$ for each $x$ and sum up all the results.

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