
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 $\{a\_n\}$, the sum of its first $n$ terms is $S\_n$. It is known that $a\_3 - a\_1 = 4$ and $S\_3 = -18$.

1. Find the general term formula for $\{a\_n\}$.
2. If $S\_k = -14$, find the value of $k$.

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