
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 a $4 \times 4$ grid, fill each cell with a distinct positive integer such that in each row and each column, there is exactly one cell where the number is equal to the sum of the numbers in the other three cells. If $M$ is the largest of these 16 positive integers, find the minimum value of $M$.

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