
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
Consider a geometric progression \\(\{a_n\}\) with a common ratio \\(q\), and let \\(S_n\\) be the sum of the first \\(n\\) terms. If \\(S_{n+1}\\), \\(S_n\\), and \\(S_{n+2}\\) form an arithmetic sequence, then the value of \\(q\\) is \_\_\_\_\_\_.

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