
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 \(\{a_n\}\) satisfying \(3a_8 = 5a_{13}\), and \(a_1 > 0\). \(S_n\) denotes the sum of the first \(n\) terms. Find the term \(n\) such that \(S_n\) is maximized for \(n \in \mathbf{N}_{+}\).

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