
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
Students in 6th grade created a winner's podium from wooden cubes, as shown in the image. How many cubes did they use in total?

The assembled podium was painted white on the entire surface (except the base), and after announcing the results, they disassembled their creation. How many cubes had 6, 5, 4, 3, 2, 1, or no white faces?

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