
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
For a geometric sequence $\{b_n\}$ with a common ratio of $4$, if $T_n$ is the product of the first $n$ terms of the sequence $\{b_n\}$, then $\frac{T_{20}}{T_{10}}$, $\frac{T_{30}}{T_{20}}$, $\frac{T_{40}}{T_{30}}$ also form a geometric sequence with a common ratio of $4^{100}$. Similarly, in an arithmetic sequence $\{a_n\}$ with a common difference of $3$, if $S_n$ is the sum of the first $n$ terms of $\{a_n\}$, then \_\_\_\_\_\_ also form an arithmetic sequence with a common difference of \_\_\_\_\_\_.

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