
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
Suppose  $ A $  is a subset of   $ n $ -elements taken from  $ 1,2,3,4,...,2009 $  such that the difference of any two numbers in  $ A $  is not a prime number. Find the largest value of   $ n $  and the set   $ A $  with this number of elements.

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