
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
We have built a large cube with edge length $n$ using $n^{3}$ unit cubes. Is there a value of $n$ for which the number of small cubes intersected by the space diagonals of the large cube is exactly half the number of small cubes not intersected by the space diagonals?

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