
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 geometric sequence $\{a\_n\}$ with a common ratio not equal to $1$, let $S\_n$ denote the sum of its first $n$ terms. Suppose that $-3a\_1, -a\_2, a\_3$ form an arithmetic sequence and $a\_1=1$. Find $S\_4$.

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