
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  $4\times4\times4$  cube is composed of  $64$  unit cubes. The faces of  $16$  unit cubes are to be coloured red. A colouring is called interesting if there is exactly  $1$  red unit cube in every  $1\times1\times 4$  rectangular box composed of  $4$  unit cubes. Determine the number of interesting colourings.

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