
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
In the arithmetic sequence $\{a_n\}$, if $a_3 + a_4 + a_5 = 12$, then $4a_3 + 2a_6 = \boxed{24}$. If the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n = 3^n - 1$, then the general term formula for $b_n = \boxed{2 \cdot 3^{n-1}}$.

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