
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 increasing sequence $\{a\_n\}$ satisfies $2a\_n=a_{n-1}+a_{n+1}$ $(n∈N^*,n > 1)$, where its first $n$ terms sum is $S\_n$. If $a\_2+a\_8=6$ and $a\_4a\_6=8$, find $S\_{10}=$ _____ .

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