
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 in the arithmetic sequence $\{a_n\}$, it is known that $\frac{a_{11}+a_{12}+\ldots+a_{20}}{10}=\frac{a_{1}+a_{2}+\ldots+a_{30}}{30}$. Then, in the geometric sequence $\{b_n\}$, there will be a similar conclusion: ______.

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