
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  $n \ge 2$  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}
user