
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
1000 identical solid cubes are combined to form one large solid cube. The surface of this large cube is painted red, and then it is divided back into 1000 smaller cubes. How many of the smaller cubes have:

- Three faces painted? 
- Only two faces painted? 
- Only one face painted? 
- No faces painted?

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