
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 an increasing arithmetic sequence $\{a_n\}$, it is known that $a_2 \cdot a_4 = 3$ and $a_1 + a_5 = 4$.
(1) Find the general term formula and the sum of the first n terms formula for the sequence $\{a_n\}$.
(2) Let $\{b_n\}$ be a sequence such that for all $n \in \mathbb{N}^*$, the equation $\frac{b_1}{3} + \frac{b_2}{3^2} + \ldots + \frac{b_n}{3^n} = a_{n+1}$ holds. Find the general term formula for the sequence $\{b_n\}$.

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