
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
Take a  $n \times n$  chess page.Determine the  $n$  such that  we can put the numbers  $1,2,3, \ldots ,n$  in the squares of the page such that we know the following two  conditions are true:

a) for each row we know all the numbers  $1,2,3, \ldots ,n$  have appeared on it and the numbers that are in the black squares of that row have the same sum as the sum of the numbers in the white squares of that row.

b) for each column we know all the numbers  $1,2,3, \ldots ,n$  have appeared on it and the numbers that are in the black squares in that column  have the same sum as the sum of the numbers in the white squares of that column.

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