
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
Each field of the table  $(mn + 1) \times (mn + 1)$  contains a real number from the interval  $[0, 1]$ . The sum the numbers in each square section of the table with dimensions  $n x n$  is equal to  $n$ . Determine how big it can be sum of all numbers in the table.

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