
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 an  $n\times{n}$  grid formed by  $n^2$  unit squares. We define the centre of a unit square as the intersection of its diagonals.
Find the smallest integer  $m$  such that, choosing any  $m$  unit squares in the grid, we always get four unit squares among them whose centres are vertices of a parallelogram.

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