
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 the arithmetic sequence $\{a_n\}$, it is known that $a_1=20$, 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) Given that the general term formula of the sequence $\{a_n\}$ is $a_n=4n-25$, 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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