
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 we place a king and a rook on a chessboard so that neither can attack the other? (The squares of the chessboard are denoted in the usual way with letters and numbers; two positions are considered different if at least one piece stands on a different square in the two positions.)

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