
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 $A$ be a non-empty subset of the set of integers. For any $k \in A$, if $k-1 \notin A$ and $k+1 \notin A$, then $k$ is called an "isolated element" of $A$. Given $S=\{1, 2, 3, 4, 5, 6, 7, 8\}$, among all sets composed of 3 elements from $S$, the number of sets that do not contain any "isolated elements" is ____.

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