
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
Consider a decreasing arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. If $a\_3a\_5=63$ and $a\_2+{a}\_{6} =16$,

(1) Find the general term formula of the sequence.
(2) For what value of $n$ does $S\_n$ reach its maximum value? Also, find the maximum value.
(3) Calculate $|a\_1|+|a\_2|+|a\_3|+…+|a\_n|$.

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