
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 the increasing sequence $\{a_n\}$ where for any $n \in \mathbb{N}^*$, it satisfies $a_n\in\mathbb{N}^*$ and $a_{a_n} = 3n$. Let $b_n = a_{2\cdot 3^{n-1}}$ ($n\in\mathbb{N}^*$), determine the sum of the first $n$ terms of the sequence $\{b_n\}$.

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