
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 the common ratio of the geometric sequence $\{a_n\}$ be $q$, and the sum of the first $n$ terms be $S_n$. If $S_{n+1}$, $S_n$, and $S_{n+2}$ form an arithmetic sequence, find the value of $q$.

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