
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 sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ are geometric sequences consisting of positive terms with common ratios $p$ and $q$ respectively, where $p > q$ and $p \neq 1, q \neq 1$. Let $c_{n} = a_{n} + b_{n}$ and $S_{n}$ be the sum of the first $n$ terms of the sequence $\left\{c_{n}\right\}$. Find $\lim _{n \rightarrow \infty} \frac{S_{n}}{S_{n-1}}$.

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