
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
A ball with a radius of 1 is placed inside a cube with an edge length of 4. The ball can move freely inside the cube, and the cube can also be flipped in any direction. What is the area of the inner surface of the cube that the ball cannot touch?

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