
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
Construct a $2 \times 2 \times 2$ cube using $5$ red unit cubes and $3$ green unit cubes. How many different ways can this be done, considering only rotations around the axes through midpoints of opposite edges and ignoring rotations around vertices and face centers?

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