
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
Let \( n \geq 2 \) be an integer, and let \( O \) be the \( n \times n \) matrix whose entries are all equal to 0. Two distinct entries of the matrix are chosen uniformly at random, and those two entries are changed from 0 to 1. Call the resulting matrix \( A \).

Determine the probability that \( A^{2} = O \), as a function of \( n \).

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