
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 2-dimensional Cartesian coordinate system, there are 16 lattice points \((i, j)\) where \(0 \leq i \leq 3\) and \(0 \leq j \leq 3\). If \(n\) points are selected from these 16 points, determine the minimum value of \(n\) such that there always exist four points which are the vertices of a square.

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