
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
Given a non-empty subset A of the set of integers, A is said to possess property M if the following conditions are satisfied: ① There exists a $k \in A$ such that $k+1 \in A$; ② For every $k \in A$, $k-2 \notin A$. Let $S = \{1,2,3,4,5,6\}$. Determine the number of subsets of $S$, each containing 3 elements, that have property M.

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