
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
Let  $k$ , $n$  be positive integers,  $k,n>1$ ,  $k<n$  and a  $n \times n$  grid of unit squares is
given. Ana and Maya take turns in coloring the grid in the following way: in each turn, a unit square is colored black in such a way that no two black cells have a common side or vertex. Find the smallest positive integer  $n$  , such that they can obtain a configuration in which each row and column contains exactly  $k$  black cells. Draw one example.

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