
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 10-digit numbers composed only of the digits 1 and 2. Divide them into two sets such that the sum of any two numbers within the same set contains at least two instances of the digit 3.

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