
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
Fill the numbers from $1$ to $25$ into a $5 \times 5$ table. Select the maximum number from each row and the minimum number from each column. A total of 10 numbers are selected in this way. Among these 10 selected numbers, there are at least $\qquad$ distinct numbers.

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