
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 a tetromino in the shape of the letter $Z$ be placed on a chessboard (size $8 \times 8$ squares) so that it is located exactly on the cells of the board and within the board's boundaries? The tetromino can be rotated and flipped. Justify your answer.

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