
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
Place five 1s, five 2s, five 3s, five 4s, and five 5s into a 5x5 grid (one number in each cell) such that the absolute difference between any two numbers in the same column does not exceed 2. Considering the sum of the numbers in each column, let the minimum value of these five sums be $M$. What is the maximum value of $M$?

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