
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
A square of side  $n$  is formed from  $n^2$  unit squares, each colored in red, yellow or green. Find minimal  $n$ , such that for each coloring, there exists a line and a column with at least 3 unit squares of the same color (on the same line or column).

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