
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
Consider the set \( S = \{1, 2, 3, \cdots, 2010, 2011\} \). A subset \( T \) of \( S \) is said to be a \( k \)-element RP-subset if \( T \) has exactly \( k \) elements and every pair of elements of \( T \) are relatively prime. Find the smallest positive integer \( k \) such that every \( k \)-element RP-subset of \( S \) contains at least one prime number.

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