
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 $S\_n$, where $a\_n > 0 (n=1,2,…)$, $a\_1=a\_2=1$, and for $n \geqslant 2$, $(a\_1+a\_2+…+a\_n)a\_n=(a\_1+a\_2+…+a\_{n-1})a\_{n+1}$. Find the value of $S\_1S\_2+S\_2S\_3+S\_3S\_4+…+S\_{n-1}S\_n=$ \_\_\_\_\_\_ .

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