
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
Adding the digits of a number to get a new number is called an operation. A number that can become 6 through several consecutive such operations is called a "good number." What is the count of "good numbers" that do not exceed 2012? What is the greatest common divisor of these "good numbers"?

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