
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

Consider an \(n \times n\) array:

\[
\begin{array}{ccccc}
1 & 2 & 3 & \cdots & n \\
n+1 & n+2 & n+3 & \cdots & 2n \\
2n+1 & 2n+2 & 2n+3 & \cdots & 3n \\
\cdots & \cdots & \cdots & \cdots & \cdots \\
(n-1)n+1 & (n-1)n+2 & (n-1)n+3 & \cdots & n^2
\end{array}
\]

Select \(x_{1}\) from this array and remove the row and column containing \(x_{1}\). Repeat this process to choose \(x_{2}\) from the remaining array, then remove the row and column containing \(x_{2}\). Continue this process until only one number \(x_{n}\) is left. Find the value of \(x_{1} + x_{2} + \cdots + x_{n}\).

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