
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 $\{a_n\}$ whose sum of the first $n$ terms is $S_n$ and satisfies $S_{15} > 0$ and $S_{16} < 0$, find the term in the set $\left\{\frac{S_1}{a_1}, \frac{S_2}{a_2}, \frac{S_3}{a_3}, \ldots, \frac{S_{15}}{a_{15}}\right\}$ that is largest.

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