
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
Consider a  $9 \times 9$  array of white squares. Find the largest  $n \in\mathbb N$  with the property: No matter how one chooses  $n$  out of 81 white squares and color in black, there always remains a  $1 \times 4$  array of white squares (either vertical or horizontal).

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