
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
Eight identical cubes with of size  $1 \times 1 \times 1$  each have the numbers  $1$  through  $6$  written on their faces with the number  $1$  written on the face opposite number  $2$ , number  $3$  written on the face opposite number  $5$ , and number  $4$  written on the face opposite number  $6$ . The eight cubes are stacked into a single  $2 \times 2 \times 2$  cube. Add all of the numbers appearing on the outer surface of the new cube. Let  $M$  be the maximum possible value for this sum, and  $N$  be the minimum possible value for this sum. Find  $M - N$ .

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