
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 sequence $\{a_n\}$ with the general term $a_n=q^{n-1}$ where $n \in \mathbb{N}^*$. Let $S_n$ denote the sum of the first $n$ terms. If $\lim_{n \to \infty} \frac{S_n}{a_{n+1}} = \frac{1}{2}$, find the value of $q$.

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