
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
Assume $A$ is a non-empty subset of the set of integers. If for some $k \in A$, both $k-1 \notin A$ and $k+1 \notin A$, then $k$ is called a "singleton" of $A$. Given that $A = \{1, 2, 3, 4, 5\}$, count the number of subsets of $A$ that have exactly one "singleton".

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