
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
The sum of the first $n$ terms of the sequence $a\_n$ is denoted as $S\_n$. Given that $S\_n = S\_{n-1} + n + 2$ for all natural numbers $n \geq 2$ and $a\_1 = 1$, find the value of $S\_5$.

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