
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
One hundred small tags with numbers are laid out in a row in increasing order: 00, 01, 02, 03, ..., 99. Then the tags are rearranged in such a way that each subsequent tag is obtained from the previous one by increasing or decreasing exactly one of the digits by 1 (for example, after 29, the next tag could be 19, 39, or 28, but not 30 or 20). What is the maximum number of tags that could remain in their original positions?

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