
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 numbers \(1,2,3, \ldots, n^{2}\) are arranged in a square table. A random number is selected from this table, and the row and column containing this number are crossed out. Then, from the remaining numbers, another number is selected, and again, the row and column containing this number are crossed out. This process continues until only one number remains in the table, which is automatically included among the selected numbers. What is the sum of all the numbers selected in this way?

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