
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
Consider an arithmetic sequence $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$. By using the summing method of adding corresponding terms in reverse order, $S_n$ can be expressed as a relation involving the first term $a_1$, the last term $a_n$, and the number of terms, namely $$S_n = \frac {(a_1 + a_n)n}{2}$$. Similarly, let $\{b_n\}$ be a geometric sequence with the product of the first $n$ terms denoted as $T_n$, where $b_n > 0 \ (n \in \mathbb{N}^*)$. By analogy to the summation method of an arithmetic sequence, express $T_n$ in terms of the first term $b_1$, the last term $b_n$, and the number of terms.

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