
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 an arithmetic sequence $\{a_n\}$, $S_{10}=50$, $S_{20}=300$. Find the general term $a_n$.
(2) Given that in a geometric sequence $\{a_n\}$ with positive terms, the sum of the first $n$ terms 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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