
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
The punch machines from before the flood punch some or even all of the nine numbered fields of a ticket. The inspectors request from the machine setter that the machine should not punch the same fields if someone places their ticket in reverse, instead of the prescribed orientation. How many such settings are possible for the machine?

$$
\begin{array}{|l|l|l|}
\hline 1 & 2 & 3 \\
\hline 4 & 5 & 6 \\
\hline 7 & 8 & 9 \\
\hline
\end{array}
$$

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