
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 large cube is constructed by arranging 64 smaller unit cubes in a 4x4x4 formation. A plane is perpendicular to one of the internal diagonals of this larger cube and bisects that diagonal. Determine the number of unit cubes that the plane intersects.
A) 30
B) 31
C) 32
D) 33
E) 34

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