
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 2 × 2 × 2 cube is to be constructed using 5 white cubes, 2 blue cubes, and 1 red cube. Determine the total number of different ways to arrange these colors in the cube, considering two constructions to be the same if one can be obtained from the other through rotation.

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