
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 box  $3\times5\times7$  is divided into unit cube cells. In each of the cells, there is a c**ockchafer. At a signal, every c**ockchafer moves through a face of its cell to a neighboring cell.

(a) What is the minimum number of empty cells after the signal?
(b) The same question, assuming that the c**ockchafers move to diagonally adjacent cells (sharing exactly one vertex).

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