
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 the cells of an $11 \times 11$ square, zeros and ones are placed such that in any shape consisting of four cells in the form of a square $\square$, the sum of the numbers is odd. (The shape can be rotated and flipped). What is the minimum number of ones that can be in such an arrangement?

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