
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
(1) In an arithmetic sequence $\{a\_n\}$, the first term is $a\_1=20$, the sum of the first $n$ terms is $S\_n$, and $S\_{10}=S\_{15}$. Find the value of $n$ for which $S\_n$ reaches its maximum value, and calculate this maximum value.
(2) The general term of the sequence $\{a\_n\}$ is given by $a\_n=4n-25$. Calculate the sum of the first $n$ terms of the sequence $\{|a\_n|\}$.

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