
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 that the geometric sequence $\{a\_n\}$ has a common ratio of $q$, and $S\_n$, $S\_{n-1}$, $S\_{n+1}$ form an arithmetic sequence, find the value of $\frac{a\_5 + a\_7}{a\_3 + a\_5}$ .

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