
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
Three rooks are randomly placed on three squares of a chessboard. Find the expected number of squares on the board that are under attack by at least one rook. Note that a rook does not attack the square it is on, but another rook can attack it.

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