
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 positive integer  $n$  such that the set  $\{502, 503, 504, . . . , 2009\}$  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  $S$ .)

*(2nd Benelux Mathematical Olympiad 2010, Problem 1)*

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