
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 $\{a_{n}\}$, where $a_{1}+a_{2}+a_{3}=-3$, and $a_{1} \cdot a_{2} \cdot a_{3}=8$.

1. Find the general term formula for the arithmetic sequence $\{a_{n}\}$.
2. If $a_{2}$, $a_{3}$, $a_{1}$ form a geometric sequence, find the sum of the first $n$ terms for the sequence $\{a_{n}+7\}$.

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