
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 composed of 64 smaller unit cubes (arranged as 4x4x4). A plane perpendicular to an internal diagonal of the large cube splits that diagonal exactly in half. Determine the number of smaller unit cubes that the plane intersects.
A) 28
B) 30
C) 32
D) 34
E) 36

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