
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 all possible ten-digit numbers that can be formed using the digits 2 and 1. Divide them into two classes such that the sum of any two numbers within each class contains at least two digits that are 3.

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