
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 factory packs its products in cubic boxes. In one store, they put  $512$  of these cubic boxes together to make a large  $8\times 8 \times 8$  cube. When the temperature goes higher than a limit in the store, it is necessary to separate the  $512$  set of boxes using horizontal and vertical plates so that each box has at least one face which is not touching other boxes. What is the least number of plates needed for this purpose?

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