
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
There are 25 people arranged in a 5x5 square matrix. Calculate the number of ways to select three people such that any two of the three are neither from the same row nor from the same column.

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