
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
1. In the arithmetic sequence $\{a\_n\}$, $S_{10}=50$, $S_{20}=300$. Find the general term $a\_n$.
2. Given that the sum of the first $n$ terms of a positive geometric sequence $\{a\_n\}$ is $S_{n}$, and $S_{3}=a_{2}+10a_{1}$, $a_{5}=81$. Find $S_{n}$.

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