
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
In a grid with 150 rows and 150 columns, numbered from 1 to 150, the shading pattern is as follows: In row 1, every box is shaded; in row 2, every second box is shaded; in row 3, every third box is shaded; this pattern continues such that every nth box in row n is shaded. Determine the column with the greatest number of shaded boxes.

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