
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 $\{a\_n\}$ satisfying $a\_1 = -11$ and $a\_4 + a\_6 = -6$,

1. Find the general term formula $a\_n$;
2. Let $S\_n$ denote the sum of the first $n$ terms of $\{a\_n\}$. Find the value of $k$ that satisfies $S\_k = 189$.

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