
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 from 1 to  $ 2013^2 $  are written row by row into a table consisting of  $ 2013 \times 2013 $  cells. Afterwards, all columns and all rows containing at least one of the perfect squares  $ 1, 4, 9, \cdots, 2013^2 $  are simultaneously deleted.
How many cells remain?

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