
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 each cell of  $5 \times 5$  table there is one number from  $1$  to  $5$  such that every number occurs exactly once in every row and in every column. Number in one column is *good positioned* if following holds:
 - In every row, every number which is left from *good positoned* number is smaller than him, and every number which is right to him is greater than him, or vice versa.
 -  In every column, every number which is above from *good positoned* number is smaller than him, and every number which is below to him is greater than him, or vice versa.
What is maximal number of good positioned numbers that can occur in this table?

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