
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
On a chessboard, numbers are assigned as shown in the diagram. How many arrangements of 8 rooks, none attacking each other, are there, in which the places occupied by the rooks contain all the numbers from 0 to 7? $\left(\begin{array}{llllllll}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0 \\ 7 & 6 & 5 & 4 & 3 & 2 & 1 & 0\end{array}\right)$

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