
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 the sequence $\{a\_n\}$ where $a\_1=8$, $a\_4=2$, and it satisfies $a\_{n+2}+a\_n=2a\_{n+1}$.
(1) The general term of the sequence $\{a\_n\}$ is $\_\_\_\_\_\_$;
(2) Let $S\_n$ be the sum of the first $n$ terms of the sequence $\{|a\_n|\}$, then $S\_n=$ $\_\_\_\_\_\_$.

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