
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
The numbers 1 and 2 are written on a blackboard. From these numbers, new numbers can be written according to the following rule: if numbers \(a\) and \(b\) are already written on the blackboard, then the number \(ab + a + b\) can be written. Is it possible to get the following numbers using this rule?
(1) 13121;
(2) 12131?

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