
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
How many non-empty subsets S of {1,2,3,...,12} have the following properties?
(1) No two consecutive integers belong to S.
(2) If S contains k elements, then every element in S is less than or equal to 2k, and none of the elements of S are prime numbers.
The prime numbers in the given set are {2,3,5,7,11}.

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