
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
Let the sum of the first $n$ terms of a geometric sequence $\{a_n\}$ be $S_n$. It is known that $S_{10} = \int (1+2x)dx$ from $0$ to $3$, and $S_{20} = 18$. Find $S_{30}$.

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