
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 rectangular board of 12 columns and 12 rows has squares numbered beginning in the upper left corner and moving left to right so row one is numbered 1 through 12, row two is 13 through 24, and so on. Determine which number of the form $n^2$ is the first to ensure that at least one shaded square is in each of the 12 columns.

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