
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
If  $N$  is the number of ways to place  $16$  *jumping*rooks on an  $8 \times 8$  chessboard such that each rook attacks exactly two other rooks, find the remainder when  $N$  is divided by  $1000$ . (A jumping rook is said to *attack*a square if the square is in the same row or in the same column as the rook.)


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