
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 a geometric sequence $\{b_n\}$ and a sequence $\{a_n\}$ satisfying $$b_{n}=3^{a_{n}}, n\in\mathbb{N}^{*}$$  
(1) Determine what type of sequence $\{a_n\}$ is and provide a proof;  
(2) If $a_{8}+a_{13}=m$, find the product $b_{1}b_{2}\ldots b_{20}$.

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