
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 that the sum of the first $n$ terms of an arithmetic sequence ${a_{n}}$ is $S_{n}$, it follows that $S_{4}$, $S_{8}-S_{4}$, $S_{12}-S_{8}$ form an arithmetic sequence. By analogy with the above conclusion, for a geometric sequence ${b_{n}}$ where the product of the first $n$ terms is $T_{n}$, it follows that $T_{4}$, _______, $\frac{T_{12}}{T_{8}}$ form a geometric sequence.

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