
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
Consider a 100-digit number consisting only of the digits 1 and 2. You are allowed to select any 10 consecutive digits and swap the positions of the first 5 with the last 5 within these 10 digits. If one 100-digit number can be transformed into another through a series of such operations, the two numbers are said to be equivalent. What is the maximum number of 100-digit numbers, each consisting only of the digits 1 and 2, that are pairwise non-equivalent?

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