
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 20-row and several-column matrix filled with 0s and 1s satisfies the following conditions: all columns are unique, and in any two columns, the rows that contain 1s in the same positions do not occur more than twice. Find the minimum number of 1s in the matrix when the number of columns is maximized.

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