
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
Petya had a large wooden cube with dimensions $30 \times 30 \times 30$ cm$^3$. Petya decided to paint the entire cube, which used 100 grams of paint. However, later Petya needed smaller cubes and cut the large cube into 27 smaller cubes with dimensions $10 \times 10 \times 10$ cm$^3$ by making 6 cuts parallel to the faces of the cube (2 cuts parallel to each pair of opposite faces). How much paint is needed to finish painting all the smaller cubes? Petya does not repaint already painted surfaces.

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