
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 $S = \{0, 1, 2, 3, 4, 5\}$, and let $A$ be a subset of $S$. If for any $x \in A$, it holds that $x-1 \notin A$ and $x+1 \notin A$, then $x$ is called an "isolated element" of set $A$. How many 4-element subsets of $S$ do not contain any "isolated elements"?

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