
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
In how many ways can two knights, one white and one black, be placed on a $16 \times 16$ chessboard so that they threaten each other? (A knight moves in an "L" shape, i.e., it can move to one of the nearest squares that is not on the same horizontal, vertical, or diagonal line.)

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