
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
Given a large \(4 \times 4 \times 4\) cube composed of 64 unit cubes, 16 of these unit cubes are to be painted red such that each \(1 \times 1 \times 4\) column within the large cube contains exactly 1 red unit cube. How many different ways can the 16 red unit cubes be selected? Explain the reasoning.

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