
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 parallelepiped is made up of identical cubes. Three faces of the parallelepiped that share a common vertex are painted. It turns out that half of all the cubes have at least one painted face. How many cubes have painted faces?

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