
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 maximum integer $N$ that satisfies the following conditions: In a $5 \times 5$ grid, any numbers from 1 to 25 are filled in, with each cell containing a different number, such that the sum of the numbers in any $2 \times 2$ subgrid is at least $N$.

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