
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 an arithmetic sequence $\{a_n\}$ be $S_n$, using the method of reverse order summation, we get: $S_n = \frac{n(a_1 + a_n)}{2}$. Similarly, let the product of the first $n$ terms of a geometric sequence $\{b_n\}$, where $b_n > 0$ ($n \in \mathbb{N}^+$), be $T_n$. Try to express $T_n$ as a relationship involving the first term $b_1$, the last term $b_n$, and the number of terms $n$, similar to the method of summing an arithmetic sequence.

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