
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
The sequence $\{a_n\}$ is an arithmetic sequence with $a_1 = 1$ and common difference $d = 2$. From this sequence, we select the 1st, 3rd, $3^2$-th, ..., $3^{n-1}$-th terms in order to form a new sequence $\{b_n\}$. The sum of the first $n$ terms of the sequence $\{b_n\}$ is ______.

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