
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 positive integer \( n \) makes it so that every \( n \)-element subset of the set \(\{1,2,3, \cdots, 2008\}\) contains 2 elements (not necessarily distinct) whose sum is a positive integer multiple of 2. What is the smallest value of \( n \)?

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