
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 six 1×1×1 cubes are painted red on each of the six faces of a 4×4×4 cube. A scoring system assigns a score as follows: 3 points for each cube with exactly 3 faces painted, 2 points for each cube with exactly 2 faces painted, 1 point for each cube with exactly 1 face painted, and -7 points for each unpainted cube, and calculate the total score for the 4×4×4 cube.

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