
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
A set of natural numbers is called "bad" if from it one can select several numbers such that their sum equals 2012. Find the smallest number \( n \) such that the numbers \( 503, 504, \ldots, 2011 \) can be partitioned into \( n \) sets in such a way that none of these sets are "bad."

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