
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
Given a sequence $\{a\_n\}$, the sum of its first $n$ terms is $S\_n$. If $a\_1=1$, and when $n\geqslant 2$, $a\_n$ is the arithmetic mean of $S\_n$ and $S\_{n-1}$, then $S\_5=$ _____ .

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