
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 larger cube is built by stacking 64 unit cubes (4x4x4). 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.

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