
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
How many ways can you assign one of the numbers \(1, 2, 3, \ldots, 10\) to each corner of a cube so that no number is used more than once and so that for each side face the sum of the numbers in the four adjacent corners is odd?

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