
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
Let \( S \) be a subset of \(\{1,2,3, \ldots, 199,200\}\). We say that \( S \) is pretty if, for every pair of elements \( a \) and \( b \) in \( S \), the number \( a - b \) is not a prime number. What is the maximum number of elements in a pretty subset of \(\{1,2,3, \ldots, 199,200\}\)?

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