
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 wooden rectangular parallelepiped with all sides measured in whole centimeters was painted red. After that, it was cut parallel to its faces into 1 cm³ cubes. It turned out that one-third of the resulting cubes had at least one face painted red, while the remaining two-thirds had all faces unpainted. Find the length of the parallelepiped if it is 2 cm longer than its width and 4 cm longer than its height.

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