
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
Let $S\_n$ be the sum of the first $n$ terms of an arithmetic sequence $\{a\_n\}$ with a non-zero common difference. If $S\_1$, $S\_2$, and $S\_4$ form a geometric sequence, find the value of $\frac{a\_2}{a\_1}$.

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