
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
In each cell of a chessboard with  $2$  rows and  $2019$  columns a real number is written so that:


- There are no two numbers written in the first row that are equal to each other.[/*]
- The numbers written in the second row coincide with (in some another order) the numbers written in the first row.[/*]
- The two numbers written in each column are different and they add up to a rational number.[/*]

Determine the maximum quantity of irrational numbers that can be in the chessboard.

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