
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 $\{a_n\}$, it is known that $\frac {a_{11}}{a_{10}} + 1 < 0$, and the sum of the first $n$ terms of the sequence, $S_n$, has a maximum value. Find the maximum value of $n$ for which $S_n > 0$.

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