
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 the set $S=\{1,2,3,4,5,6,7,8\}$, for $x\in S$, if $x+1 \notin S$ and $x-1 \notin S$, then $x$ is a "good element" of $S$. Among all sets composed of $3$ elements from $S$, the number of sets that do not contain any "good elements" is ____.

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