
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
Let $\{a_{n}\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. Given $a_{2}+a_{6}=2$ and $S_{9}=-18$. <br/>$(1)$ Find $a_{n}$; <br/>$(2)$ For what value of $n$, is $|S_{n}|$ minimized? And find this minimum value.

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