
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
In an arithmetic sequence \(\left\{a_{n}\right\}\), if \(\frac{a_{11}}{a_{10}} < -1\), and its partial sum \(S_{n}\) has a maximum value, then when \(S_{n}\) attains its smallest positive value, \(n = \) \(\qquad\).

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