
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 $\left\{a_{n}\right\}$, given $\left|a_{5}\right|=\left|a_{11}\right|$ and $d>0$, find the positive integer value of $n$ that minimizes the sum of the first $n$ terms, $S_{n}$.

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