
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 a large cube of dimensions \(4 \times 4 \times 4\) composed of 64 unit cubes. Select 16 of these unit cubes and color them red, ensuring that within every \(1 \times 1 \times 4\) rectangular prism formed by 4 unit cubes, exactly 1 unit cube is colored red. How many different ways can the 16 unit cubes be colored red? Provide a justification for your answer.

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