
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, each small cell is filled with either the number 1 or 2. If the sum of the numbers in any \(3 \times 3\) subgrid (there are 4 such subgrids) is divisible by 4, and the sum of the numbers in all 16 cells is not divisible by 4, find the maximum and minimum values of the sum of these 16 numbers.

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