
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 the arithmetic sequence $\{a\_n\}$, where $a\_1 = -3$ and $11a\_5 = 5a\_8$. Let $S\_n$ denote the sum of the first $n$ terms.

1. Find $a\_n$;
2. For what value of $n$ is $S\_n$ minimum? And find the minimum value of $S\_n$.

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