
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 the arithmetic sequence $\{a\_n\}$, the sum of the first $n$ terms is $S\_n$. If $S\_{15} > 0$ and $S\_{16} < 0$, determine the maximum value among $\frac{S\_1}{a\_1}$, $\frac{S\_2}{a\_2}$, ..., $\frac{S\_{15}}{a\_{15}}$.

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