
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 the arithmetic sequence $\{a\_n\}$, $a\_{16} + a\_{17} + a\_{18} = a\_9 = -36$, and the sum of its first $n$ terms is $S\_n$.

1. Find the general term formula for the sequence $\{a\_n\}$ and the sum of its first $n$ terms $S\_n$.
2. Find the minimum value of $S\_n$ and the value of $n$ when $S\_n$ reaches its minimum.

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