
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 are there to place 3 rooks on the board shown in the picture such that they do not attack each other? A rook attacks all squares in the row and column it stands on. A rook cannot attack through the cut-out squares horizontally. 

![](https://cdn.mathpix.com/cropped/2024_05_06_f1445201e81a69006a8ag-04.jpg?height=237&width=511&top_left_y=2389&top_left_x=824)

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