
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 $1$s, five $2$s, five $3$s, five $4$s, and five $5$s into a $5 \times 5$ grid (one number per cell) such that the absolute difference between any two numbers in the same column does not exceed $2$. Let $M$ be the minimum value of the sum of the five numbers in each column. Find the maximum value of $M$.

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