
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 $S_n$ be the sum of the first $n$ terms of an arithmetic sequence with common difference $d$. Then the sequence $S_6 - S_3$, $S_9 - S_6$, $S_{12} - S_9$ is an arithmetic sequence with common difference $9d$. By analogous reasoning, conclude that: Let $T_n$ be the product of the first $n$ terms of a geometric sequence with common ratio $2$, then the sequence $$\frac{T_{6}}{T_{3}}, \frac{T_{9}}{T_{6}}, \frac{T_{12}}{T_{9}}$$ is a geometric sequence, and its common ratio is _______.

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