
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 an arithmetic sequence $\{a_n\}$, the sum of the first 10 terms is $\frac{125}{7}$, and the sum of the first 20 terms is $- \frac{250}{7}$.  
(1) Find the sum of the first $n$ terms, $S_n$.  
(2) Find the value of $n$ which maximizes $S_n$.

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