
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]


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We know that arithmetic sequences and geometric sequences have similar properties in many aspects. Please derive the formula for the product of the first n terms of a positive geometric sequence {b<sub>n</sub>}, denoted as T<sub>n</sub>, by analogy with the formula for the sum of the first n terms of an arithmetic sequence {a<sub>n</sub>}, denoted as S<sub>n</sub>, which is S<sub>n</sub>\= $$\frac {n(a_{1}+a_{n})}{2}$$.

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