
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
Jill has some unit cubes which are all black, grey, or white. She uses 27 of them to build a 3 × 3 × 3 cube. She wants the surface to be exactly one-third black, one-third grey, and one-third white. The smallest possible number of black cubes she can use is \(X\) and the largest possible number of black cubes she can use is \(Y\). What is the value of \(Y - X\)?

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