
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 finite set of integers is called bad if its elements add up to 2010. A finite set of integers is a Benelux-set if none of its subsets is bad. Determine the smallest integer \( n \) such that the set \( \{502, 503, 504, \ldots, 2009\} \) can be partitioned into \( n \) Benelux-sets. 

(A partition of a set \( S \) into \( n \) subsets is a collection of \( n \) pairwise disjoint subsets of \( S \), the union of which equals \( S \).)

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