
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
When a piece of paper with digits written on it is turned upside down, the digits $0, 1, 8$ remain the same, while $6$ and $9$ switch places and all other digits do not make sense when viewed upside down. Find the number of 9-digit numbers that remain the same when the piece of paper is turned upside down.

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