
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 the set $S=\{0,1,2,3,4,5\}$, and let $A$ be a subset of $S$. If for an element $x \in A$, it holds that $x-1 \notin A$ and $x+1 \notin A$, then $x$ is referred to as an "isolated element" of set $A$. Determine the number of 4-element subsets of $S$ that have no "isolated elements".

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