
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
Consider the set $S = \{1, 2, 3, 4, 5, 6\}$. A subset $A$ of $S$ is given. If $x \in A$ and both $x - 1 \notin A$ and $x + 1 \notin A$, then $x$ is considered an "isolated element" of $A$. Determine the number of 4-element subsets of $S$ that contain no "isolated elements".

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