
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
Consider an $8 \times 8 \times 8$ Rubik's cube where each face is painted a different color, and any layer can be turned. Let $X$ be a move that rotates the shaded layer (indicated by arrows going from the top to the right of the cube) clockwise by 90 degrees around the $X$ axis. Let $Y$ be a move that rotates another shaded layer (indicated by arrows going from the front to the top) clockwise by 90 degrees around the $Y$ axis. 

Define move $M$ as performing $X$ followed by $Y$. If the cube starts in solved form, what is the smallest number of repetitions of $M$ required for the cube to return to its original solved state?

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