
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
Petya and Vasya play the following game. Petya thinks of a natural number \( x \) with the sum of its digits being 2012. In one move, Vasya selects any natural number \( a \) and finds out from Petya the sum of the digits of the number \( |x-a| \). What is the minimum number of moves Vasya needs to make to guarantee determining \( x \)?

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