
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
Determine the largest natural number  $ N $  having the following property: every  $ 5\times 5 $  array consisting of pairwise distinct natural numbers from  $ 1 $  to  $ 25 $  contains a  $ 2\times 2 $  subarray of numbers whose sum is, at least,  $ N. $ *Demetres Christofides* and *Silouan Brazitikos*

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